GRE Quantitative Quiz: Coordinate Geometry Graph Interpretation
20 questions · exam conditions
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Coordinate Geometry Graph InterpretationQuestion 1 of 20

A line has equation 2x+5y=102x+5y=10. What is the slope of the line?

−25-\frac{2}{5}
25\frac{2}{5}
−52-\frac{5}{2}
52\frac{5}{2}
1010
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GRE Quantitative Quiz

GRE Quantitative Quiz: Coordinate Geometry Graph Interpretation

Practice Coordinate Geometry Graph Interpretation in GRE Quantitative with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Coordinate Geometry Graph Interpretation, giving you a quick way to practice the rules, question types, and explanations that matter most for GRE Quantitative.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

A line has equation 2x+5y=102x+5y=10. What is the slope of the line?

  1. −25-\frac{2}{5} (correct answer)
  2. 25\frac{2}{5}
  3. −52-\frac{5}{2}
  4. 52\frac{5}{2}
  5. 1010
Explanation: This question tests graph interpretation, requiring the slope from a line equation in standard form. To find the slope, rewrite 2x + 5y = 10 as y = -2/5 x + 2, where -2/5 is the slope. This form highlights the negative slope and y-intercept of 2. Applying the conversion confirms the slope as -2/5. Thus, the correct answer is -2/5, choice A. A common incorrect option is -5/2, from swapping numerator and denominator. Another mistake could be forgetting the negative sign, leading to 2/5.

Question 2

Which point lies on the graph of the line 2x+y=12x+y=1?

  1. (1,1)(1,1)
  2. (0,1)(0,1) (correct answer)
  3. (1,−3)(1,-3)
  4. (−1,3)(-1,3)
  5. (2,−1)(2,-1)
Explanation: This question tests coordinate geometry by asking which point satisfies a linear equation. To check if a point lies on the line 2x + y = 1, we substitute the x and y coordinates into the equation. For point (0,1): 2(0) + 1 = 0 + 1 = 1, which equals the right side, so this point lies on the line. We can verify other options don't work: for (1,1), we get 2(1) + 1 = 3 ≠ 1. The key is systematically substituting each point's coordinates and checking if the equation holds true.

Question 3

Line pp has equation y=−2x+9y=-2x+9. Line qq is obtained by shifting the graph of line pp up 4 units. Which of the following is an equation of line qq?

  1. y=−2x+5y=-2x+5
  2. y=−2x+13y=-2x+13 (correct answer)
  3. y=2x+13y=2x+13
  4. y=−6x+9y=-6x+9
  5. y=−2x−13y=-2x-13
Explanation: This question tests coordinate geometry, involving vertical shifts in line equations. Shifting up by 4 units adds 4 to the y-intercept of y = -2x + 9, resulting in y = -2x + 13. The slope remains unchanged, only the constant term increases. This new equation reflects the parallel line above the original. Therefore, Choice B is correct. A common incorrect option is y = -2x + 5, from subtracting instead of adding. Another error might involve altering the slope, leading to options like y = 2x + 13.

Question 4

Line pp has equation y=−13x+4y=-\frac{1}{3}x+4. What is the yy-intercept of line pp?

  1. −13-\frac{1}{3}
  2. 13\frac{1}{3}
  3. −4-4
  4. 44 (correct answer)
  5. (4,0)(4,0)
Explanation: This question tests coordinate geometry, specifically identifying the y-intercept from a line equation. In the equation y = -1/3x + 4, which is in slope-intercept form y = mx + b, the constant term b represents the y-intercept. The y-intercept is 4, which is the y-value when x = 0: y = -1/3(0) + 4 = 4. This means the line crosses the y-axis at the point (0,4). Students often confuse the slope (-1/3) with the y-intercept or mistakenly write the y-intercept as a coordinate pair like (4,0).

Question 5

A line has equation y=−32x+6y= -\frac{3}{2}x+6. If the line is shifted right by 2 units (with no vertical shift), which of the following is an equation of the new line?

  1. y=−32x+3y=-\frac{3}{2}x+3
  2. y=−32x+9y=-\frac{3}{2}x+9
  3. y=−32(x−2)+6y=-\frac{3}{2}(x-2)+6 (correct answer)
  4. y=−32(x+2)+6y=-\frac{3}{2}(x+2)+6
  5. y=32x+6y=\frac{3}{2}x+6
Explanation: This question tests graph interpretation, applying a horizontal shift to the line y = -3/2 x + 6. Shifting right by 2 replaces x with (x-2), yielding y = -3/2 (x-2) + 6. This maintains the slope but adjusts the intercept. Expanding gives y = -3/2 x + 9, equivalent to the form in C. Therefore, Choice C is correct. A common mistake is shifting left, leading to (x+2). Another error could be vertical shift confusion, altering the constant incorrectly.

Question 6

The line with equation 3x+2y=123x+2y=12 is graphed in the xyxy-plane. What is the yy-intercept of the line?​

  1. 66 (correct answer)
  2. −6-6
  3. 44
  4. −4-4
  5. 32\frac{3}{2}
Explanation: This question tests graph interpretation, specifically finding the y-intercept from a linear equation in standard form. The y-intercept occurs where the line crosses the y-axis, which is when x = 0. Substituting x = 0 into 3x + 2y = 12 gives: 3(0) + 2y = 12, so 2y = 12, and y = 6. Therefore, the y-intercept is 6, or the point (0,6). A common mistake is confusing the y-intercept with the x-intercept (which would be 4) or misidentifying coefficients as intercepts.

Question 7

Line ss passes through (2,−1)(2,-1) and (2,5)(2,5). Which of the following best describes the graph of line ss?

  1. A horizontal line with equation y=2y=2
  2. A vertical line with equation x=2x=2 (correct answer)
  3. A line with slope 22 and yy-intercept −1-1
  4. A line with slope −2-2 and yy-intercept 55
  5. A line with equation y=x+2y=x+2
Explanation: This question tests graph interpretation, identifying a vertical line from points with same x-coordinate. Points (2,-1) and (2,5) share x=2, indicating a vertical line x=2 with undefined slope. Vertical lines are perpendicular to the x-axis. This describes the graph accurately. Thus, Choice B is correct. A common incorrect option is horizontal line y=2, confusing x and y. Another mistake might involve calculating a finite slope, leading to other options.

Question 8

Which of the following describes the graph of the equation y=2x+5y=2x+5 in the coordinate plane?

  1. A line with slope 55 and yy-intercept 22
  2. A line with slope −2-2 and yy-intercept 55
  3. A line with slope 22 and yy-intercept −5-5
  4. A line with slope 22 and yy-intercept 55 (correct answer)
  5. A line that crosses the xx-axis at x=5x=5
Explanation: This question tests graph interpretation by asking to identify key features of a linear equation. The equation y = 2x + 5 is in slope-intercept form y = mx + b, where m = 2 is the slope and b = 5 is the y-intercept. This describes a line that rises 2 units vertically for every 1 unit horizontally and crosses the y-axis at (0,5). The correct answer is a line with slope 2 and y-intercept 5. Common errors include reversing the slope and y-intercept values or confusing the y-intercept with the x-intercept.

Question 9

Two lines are given by y=34x+1y=\frac{3}{4}x+1 and y=34x−5y=\frac{3}{4}x-5. Which of the following best describes the relationship between the two lines?

  1. They intersect at exactly one point.
  2. They are perpendicular.
  3. They are parallel and distinct. (correct answer)
  4. They are the same line.
  5. They intersect on the yy-axis.
Explanation: This question tests graph interpretation, comparing slopes and intercepts to determine line relationships. Both lines have slope 3/4 but different y-intercepts (1 and -5), indicating they are parallel and distinct. Parallel lines never intersect and maintain constant distance. This relationship is confirmed by the identical slopes and unequal intercepts. Thus, Choice C is correct. A common mistake is assuming they intersect at one point due to similar slopes. Another error could be thinking they are the same line if intercepts are miscompared.

Question 10

The line y=x−4y=x-4 is shifted upward by 66 units to form a new line. What is the yy-intercept of the new line?

  1. −10-10
  2. −6-6
  3. 22 (correct answer)
  4. 44
  5. 1010
Explanation: This question tests graph interpretation, specifically understanding vertical translations of linear functions. The original line y = x - 4 has y-intercept -4 (when x = 0, y = -4). When a line is shifted upward by 6 units, we add 6 to the entire equation: y = x - 4 + 6 = x + 2. The new line has equation y = x + 2, so its y-intercept is 2. This vertical shift moves every point on the line up by 6 units, including the y-intercept which moves from -4 to 2. A common error is subtracting instead of adding the shift amount.

Question 11

A line has equation y=23x+4y=\frac{2}{3}x+4. Which of the following describes the graph of the line?

  1. It has negative slope and crosses the yy-axis at 44.
  2. It has positive slope and crosses the yy-axis at −4-4.
  3. It has positive slope and crosses the yy-axis at 44. (correct answer)
  4. It has slope 44 and crosses the yy-axis at 23\frac{2}{3}.
  5. It is a horizontal line at y=23y=\frac{2}{3}.
Explanation: This question tests graph interpretation, describing slope and intercept from y = 2/3 x + 4. The positive slope 2/3 indicates rising left to right, with y-intercept at 4. This matches a line crossing y-axis at (0,4). Analysis confirms positive slope and intercept. Thus, Choice C is correct. A common incorrect option is negative slope due to sign confusion. Another mistake might involve swapping slope and intercept values.

Question 12

A line has equation y=3x−7y=3x-7. What is the yy-intercept of the line?

  1. 33
  2. −7-7 (correct answer)
  3. 77
  4. −73-\frac{7}{3}
  5. (0,7)(0,7)
Explanation: This question tests graph interpretation, specifically identifying the y-intercept from a line equation in slope-intercept form. The equation y = 3x - 7 is already in the form y = mx + b, where b is the y-intercept. The y-intercept occurs when x = 0, giving y = 3(0) - 7 = -7. Therefore, the y-intercept is -7, which represents the point where the line crosses the y-axis. A common mistake is confusing the slope (3) with the y-intercept or misidentifying the sign, thinking the y-intercept is positive 7.

Question 13

On the coordinate plane, a line is described as crossing the yy-axis at (0,−2)(0,-2) and the xx-axis at (5,0)(5,0). What is the slope of the line?

  1. 25\frac{2}{5} (correct answer)
  2. −25-\frac{2}{5}
  3. −52-\frac{5}{2}
  4. 52\frac{5}{2}
  5. −2-2
Explanation: This question tests graph interpretation, calculating slope from x- and y-intercepts. The points (0,-2) and (5,0) give slope m = (0 - (-2))/(5 - 0) = 2/5. This positive slope shows the line rising from left to right. Applying the formula confirms this value. Therefore, Choice A is correct. A common incorrect option is -2/5, from neglecting the double negative. Another mistake might be inverting to 5/2.

Question 14

Line mm has equation y=−4x+9y=-4x+9. What is the slope of line mm?

  1. 99
  2. 44
  3. −4-4 (correct answer)
  4. −94-\frac{9}{4}
  5. 94\frac{9}{4}
Explanation: This question tests graph interpretation, specifically identifying the slope from a line equation in slope-intercept form. The equation y = -4x + 9 follows the pattern y = mx + b, where m is the slope and b is the y-intercept. The coefficient of x is -4, so the slope is -4. This means the line decreases by 4 units vertically for every 1 unit increase horizontally. A common error is confusing the slope with the y-intercept (9) or misreading the negative sign, leading to answers like 4 or 9/4.

Question 15

Line mm has equation y=3x−7y=3x-7. What is the yy-intercept of line mm?

  1. 33
  2. −7-7 (correct answer)
  3. 77
  4. −73-\frac{7}{3}
  5. −3-3
Explanation: This question tests graph interpretation, focusing on identifying the y-intercept from a line's equation in slope-intercept form. The y-intercept is the value of y where the line crosses the y-axis, represented by the constant term b in y = mx + b. For the equation y = 3x - 7, the slope m is 3, and the y-intercept b is -7. This directly gives the y-intercept as -7. Therefore, the correct answer is -7, which is choice B. A common mistake is confusing the y-intercept with the slope, leading to selecting 3. Another error might involve misreading the sign, resulting in choices like 7.

Question 16

Which point is below the line y=2x−1y=2x-1 and above the x-axis?

  1. (1, 1)
  2. (2, 1) (correct answer)
  3. (2, 3)
  4. (0, 1)
Explanation: At x = 2, the line y = 2x - 1 gives y = 3, so the point (2, 1) has y = 1 below 3 and above the x-axis. A tempting wrong point is (1, 1), but at x = 1 the line also gives y = 1, so that point lies on the line, not below it.

Question 17

Lines y=2x−5y=2x-5 and y=−x+1y=-x+1 intersect. In which quadrant is the intersection?

  1. Quadrant I
  2. Quadrant II
  3. Quadrant III
  4. Quadrant IV (correct answer)
Explanation: Set the two y-values equal: 2x - 5 = -x + 1. Solving gives 3x = 6, so x = 2. Substituting into either line gives y = -1. Since x is positive and y is negative, the point (2, -1) lies in Quadrant IV. The tempting wrong answer is Quadrant I, where both coordinates are positive, but here y is negative.

Question 18

Line L has x-intercept -3 and y-intercept 5. What is the slope of a line perpendicular to L?

  1. -3/5 (correct answer)
  2. 3/5
  3. 5/3
  4. -5/3
Explanation: A line with x-intercept -3 and y-intercept 5 passes through (-3,0) and (0,5). Its slope is (5-0)/(0-(-3)) = 5/3. A perpendicular line has slope the negative reciprocal, so the answer is -3/5. The tempting wrong answer is 5/3, which is the slope of L itself, not the perpendicular line.

Question 19

Graph of y=f(x)y=f(x) contains (−2,3)(-2,3). If g(x)=f(x+1)−2g(x)=f(x+1)-2, which point must be on the graph of gg?

  1. (-3, 1) (correct answer)
  2. (-1, 1)
  3. (-3, 5)
  4. (-1, 5)
Explanation: Since g(-3)=f(-3+1)-2=f(-2)-2=3-2=1, the point (-3,1) must be on the graph of g. The tempting wrong answer is (-1,1), which comes from shifting right instead of left; the inside +1 shifts the graph left by 1, not right.

Question 20

Circle C has center (2,−3)(2,-3) and passes through (−2,0)(-2,0). If its radius is increased by 2, what is the increase in area?

  1. 25π
  2. 49π
  3. 24π (correct answer)
  4. 4π
Explanation: Use the distance formula to find the radius: from (2,-3) to (-2,0) is 5. Increasing the radius by 2 makes it 7, so the old area is 25π and the new area is 49π. The increase is 49π - 25π = 24π. Don't pick 49π; that's the new total area, not the amount of increase.