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Intermediate Geometry : Coordinate Geometry

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Example Questions

Example Question #251 : Coordinate Geometry

Find the x-intercept of the line 19x+5y=2 .

Possible Answers:

$(-\frac{15}{19},0)$

$(-\frac{19}{2},0)$

$(\frac{5}{19},0)$

$(\frac{2}{19},0)$

Correct answer:

$(\frac{2}{19},0)$

Explanation:

Start by putting the equation into y=mx+b form, where is the slope, and is the y-intercept.

19x+5y=2

5y=-19x+2

$y=-\frac{19}{5}x+\frac{2}{5}$

By definition, the x-intercept is where the line crosses the x-axis. As such, the y-coordinate of this point must be .

Plug in for in the equation for this line.

$0=-\frac{19}{5}x+\frac{2}{5}$

Now, solve for .

$\frac{19}{5}x=\frac{2}{5}$

$x=\frac{2}{19}$

The x-intercept is found at $(\frac{2}{19}, 0)$ .

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Example Question #21 : How To Find X Or Y Intercept

Find the x-intercept for the line 8x-9y=12 .

Possible Answers:

(2, 0)

$(-\frac{1}{2},0)$

$(\frac{3}{2},0)$

$(-\frac{2}{3},0)$

Correct answer:

$(\frac{3}{2},0)$

Explanation:

Start by putting the equation into y=mx+b form, where is the slope, and is the y-intercept.

8x-9y=12

9y+12=8x

9y=8x-12

$y=\frac{8}{9}x-\frac{4}{3}$

By definition, the x-intercept is where the line crosses the x-axis. As such, the y-coordinate of this point must be .

Plug in for in the equation for this line.

$0=\frac{8}{9}x-\frac{4}{3}$

Now, solve for .

$\frac{8}{9}x=\frac{4}{3}$

$x=\frac{3}{2}$

The x-intercept is found at $(\frac{3}{2}, 0)$ .

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Example Question #1531 : Intermediate Geometry

Find the x-intercept for the line -8x+2y=1 .

Possible Answers:

$(-\frac{1}{4},0)$

$(-\frac{1}{8},0)$

$(-\frac{1}{2},0)$

$(-\frac{3}{8},0)$

Correct answer:

$(-\frac{1}{8},0)$

Explanation:

Start by putting the equation into y=mx+b form, where is the slope, and is the y-intercept.

-8x+2y=1

2y=8x+1

$y=4x+\frac{1}{2}$

By definition, the x-intercept is where the line crosses the x-axis. As such, the y-coordinate of this point must be .

Plug in for in the equation for this line.

$0=4x+\frac{1}{2}$

Now, solve for .

$4x=-\frac{1}{2}$

$x=-\frac{1}{8}$

The x-intercept is found at $(-\frac{1}{8}, 0)$ .

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Example Question #31 : X And Y Intercept

Find the x-intercept of the line -5x-6y=23 .

Possible Answers:

$(-\frac{23}{5},0)$

$(-\frac{115}{36},0)$

$(-\frac{12}{5},0)$

$(-\frac{17}{5},0)$

Correct answer:

$(-\frac{23}{5},0)$

Explanation:

Start by putting the equation into y=mx+b form, where is the slope, and is the y-intercept.

-5x-6y=23

6y+23=-5x

6y=-5x-23

$y=-\frac{5}{6}x-\frac{23}{6}$

By definition, the x-intercept is where the line crosses the x-axis. As such, the y-coordinate of this point must be .

Plug in for in the equation for this line.

$0=-\frac{5}{6}x-\frac{23}{6}$

Now, solve for .

$\frac{5}{6}x=-\frac{23}{6}$

$x=-\frac{23}{5}$

The x-intercept is found at $(-\frac{23}{5}, 0)$ .

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Example Question #32 : X And Y Intercept

Find the x-intercept for the line 4x-9y=15 .

Possible Answers:

$(\frac{17}{4},0)$

(4, 0)

(3, 0)

$(\frac{15}{4}, 0)$

Correct answer:

$(\frac{15}{4}, 0)$

Explanation:

Start by putting the equation into y=mx+b form, where is the slope, and is the y-intercept.

4x-9y=15

15+9y=4x

9y=4x-15

$y=\frac{4}{9}x-\frac{5}{3}$

By definition, the x-intercept is where the line crosses the x-axis. As such, the y-coordinate of this point must be .

Plug in for in the equation for this line.

$0=\frac{4}{9}x-\frac{5}{3}$

Now, solve for .

$\frac{4}{9}x=\frac{5}{3}$

$x=\frac{15}{4}$

The x-intercept is found at $(\frac{15}{4}, 0)$ .

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Example Question #1541 : Intermediate Geometry

Find the x-intercept of the line -9x+21y=27 .

Possible Answers:

(-6, 0)

(-1, 0)

(12, 0)

(-3, 0)

Correct answer:

(-3, 0)

Explanation:

Recall that an x-intercept occurs when the line crosses the x-axis. Thus, the y-coordinate of the x-intercept must be .

Plug in for the y-value.

-9x+21y=27

-9x+21(0)=27

-9x=27

x=-3

The x-intercept is located at (-3, 0) .

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Example Question #1542 : Intermediate Geometry

Find the x-intercept of the line 4x-12y=28 .

Possible Answers:

(10, 0)

(4, 0)

(7, 0)

(14, 0)

Correct answer:

(7, 0)

Explanation:

Recall that an x-intercept occurs when the line crosses the x-axis. Thus, the y-coordinate of the x-intercept must be .

Plug in for the y-value.

4x-12y=28

4x-12(0)=28

4x=28

x=7

The x-intercept is located at (7, 0) .

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Example Question #31 : How To Find X Or Y Intercept

Find the x-intercept for the line y=12x-24 .

Possible Answers:

(-2, 0)

(4, 0)

(1, 0)

(2, 0)

Correct answer:

(2, 0)

Explanation:

Recall that an x-intercept occurs when the line crosses the x-axis. Thus, the y-coordinate of the x-intercept must be .

Plug in for the y-value.

y=12x-24

12x-24=0

12x=24

x=2

The x-intercept is located at (2, 0) .

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Example Question #1544 : Intermediate Geometry

Find the x-intercept of the line -x+10y=22 .

Possible Answers:

(24, 0)

(13, 0)

(-11, 0)

(-22, 0)

Correct answer:

(-22, 0)

Explanation:

Recall that an x-intercept occurs when the line crosses the x-axis. Thus, the y-coordinate of the x-intercept must be .

Plug in for the y-value.

-x+10y=22

-x+10(0)=22

-x=22

x=-22

The x-intercept is located at (-22, 0) .

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Example Question #31 : How To Find X Or Y Intercept

Find the x-intercept of the line -2x+10y=122 .

Possible Answers:

(-59, 0)

(-62, 0)

(-60, 0)

(-61, 0)

Correct answer:

(-61, 0)

Explanation:

Recall that an x-intercept occurs when the line crosses the x-axis. Thus, the y-coordinate of the x-intercept must be .

Plug in for the y-value.

-2x+10y=122

-2x+10(0)=122

-2x=122

x=-61

The x-intercept is located at (-61, 0) .

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Intermediate Geometry : Coordinate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #251 : Coordinate Geometry

Example Question #21 : How To Find X Or Y Intercept

Example Question #1531 : Intermediate Geometry

Example Question #31 : X And Y Intercept

Example Question #32 : X And Y Intercept

Example Question #1541 : Intermediate Geometry

Example Question #1542 : Intermediate Geometry

Example Question #31 : How To Find X Or Y Intercept

Example Question #1544 : Intermediate Geometry

Example Question #31 : How To Find X Or Y Intercept

All Intermediate Geometry Resources

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