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Intermediate Geometry : Coordinate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

Example Question #46 : How To Find X Or Y Intercept

Find the x-intercept of the line -12x+3y=2 .

Possible Answers:

(-6, 0)

$\left(-\frac{1}{3}, 0\right)$

$\left(-\frac{1}{6}, 0\right)$

$\left(\frac{1}{4}, 0\right)$

Correct answer:

$\left(-\frac{1}{6}, 0\right)$

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.

-12x+3y=2

-12x+3(0)=2

-12x=2

$x=-\frac{1}{6}$

The x-intercept is located at $\left(-\frac{1}{6}, 0\right)$ .

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Example Question #47 : How To Find X Or Y Intercept

Find the x-intercept of the line 16x+20y=4 .

Possible Answers:

$\left(\frac{1}{4}, 0\right)$

$\left(\frac{1}{12}, 0\right)$

$\left(\frac{1}{8}, 0\right)$

$\left(\frac{1}{2}, 0\right)$

Correct answer:

$\left(\frac{1}{4}, 0\right)$

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.

16x+20y=4

16x+20(0)=4

16x=4

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

The x-intercept is located at $\left(\frac{1}{4}, 0\right)$ .

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Example Question #271 : Coordinate Geometry

Find the x-intercept of the line 15x-3y=12 .

Possible Answers:

$\left(\frac{4}{5}, 0\right)$

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

$\left(\frac{3}{5}, 0\right)$

$\left(\frac{3}{4}, 0\right)$

Correct answer:

$\left(\frac{4}{5}, 0\right)$

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.

15x-3y=12

15x-3(0)=12

15x=12

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

The x-intercept is located at $\left(\frac{4}{5}, 0\right)$ .

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Example Question #272 : Coordinate Geometry

Find the x-intercept of the line $\frac{1}{9}x-20y=12$ .

Possible Answers:

(-216, 0)

(152, 0)

$\left(\frac{4}{3}, 0\right)$

(108, 0)

Correct answer:

(108, 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.

$\frac{1}{9}x-20y=12$

$\frac{1}{9}x-20(0)=12$

$\frac{1}{9}x=12$

x=108

The x-intercept is located at (108, 0) .

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Example Question #52 : How To Find X Or Y Intercept

Find the x-intercept for the line 16x-18y=22 .

Possible Answers:

$\left(\frac{11}{9}, 0\right)$

$\left(\frac{11}{10}, 0\right)$

$\left(-\frac{8}{11}, 0\right)$

$\left(\frac{11}{8}, 0\right)$

Correct answer:

$\left(\frac{11}{8}, 0\right)$

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.

16x-18y=22

16x-18(0)=22

16x=22

$x=\frac{11}{8}$

The x-intercept is located at $\left(\frac{11}{8}, 0\right)$ .

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Example Question #273 : Coordinate Geometry

Find the y-intercept of the line 13x-10y=12 .

Possible Answers:

$\left(0, -\frac{6}{5}\right)$

$\left(0, \frac{4}{5}\right)$

(0, 2)

$\left(0, \frac{5}{6}\right)$

Correct answer:

$\left(0, -\frac{6}{5}\right)$

Explanation:

Recall that at the y-intercept, the line crosses the y-axis. This means that at the y-intercept, the value of the x-coordinate is .

Plug in for into the equation to find the y-intercept.

13x-10y=12

13(0)-10y=12

-10y=12

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

The y-intercept for this line is $\left(0, -\frac{6}{5}\right)$ .

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Example Question #54 : How To Find X Or Y Intercept

Find the y-intercept of the line 14x-12y=28 .

Possible Answers:

$\left(0, -\frac{5}{3}\right)$

$\left(0, \frac{3}{7}\right)$

$\left(0, -\frac{7}{3}\right)$

(0, -2)

Correct answer:

$\left(0, -\frac{7}{3}\right)$

Explanation:

Recall that at the y-intercept, the line crosses the y-axis. This means that at the y-intercept, the value of the x-coordinate is .

Plug in for into the equation to find the y-intercept.

14x-12y=28

14(0)-12y=28

-12y=28

$y=-\frac{7}{3}$

The y-intercept for this line is $\left(0, -\frac{7}{3}\right)$ .

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Example Question #274 : Coordinate Geometry

Find the y-intercept of the line 15x+10y=-2 .

Possible Answers:

$\left(0, -\frac{2}{5}\right)$

$\left(0, -\frac{1}{5}\right)$

$\left(0, \frac{3}{5}\right)$

(0, -5)

Correct answer:

$\left(0, -\frac{1}{5}\right)$

Explanation:

Recall that at the y-intercept, the line crosses the y-axis. This means that at the y-intercept, the value of the x-coordinate is .

Plug in for into the equation to find the y-intercept.

15x+10y=-2

15(0)+10y=-2

10y=-2

$y=-\frac{1}{5}$

The y-intercept for this line is $\left(0, -\frac{1}{5}\right)$ .

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Example Question #275 : Coordinate Geometry

Find the y-intercept of the line $-14x+\frac{1}{4}y=2$ .

Possible Answers:

$\left(0, \frac{1}{2}\right)$

(0, 4)

(0, 8)

(0, 6)

Correct answer:

(0, 8)

Explanation:

Recall that at the y-intercept, the line crosses the y-axis. This means that at the y-intercept, the value of the x-coordinate is .

Plug in for into the equation to find the y-intercept.

$-14x+\frac{1}{4}y=2$

$-14(0)+\frac{1}{4}y=2$

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

y=8

The y-intercept for this line is (0, 8) .

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Example Question #276 : Coordinate Geometry

Given the following table of a linear function, find the y-intercept.

x	f(x)
-2	-59
4	91
6	141
12	291

Possible Answers:

Correct answer:

Explanation:

Start by taking a pair of points and find the slope of the line.

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\text{Slope}=\frac{91-(-59)}{4-(-2)}=\frac{150}{6}=25$

Next, re-write the equation in point-slope form.

y-(-59)=25(x-(-2))

Rewrite this equation so that it is in slope-intercept form.

y+59=25(x+2)

y+59=25x+50

y=25x-9

The y-intercept for this line is .

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Intermediate Geometry : Coordinate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #46 : How To Find X Or Y Intercept

Example Question #47 : How To Find X Or Y Intercept

Example Question #271 : Coordinate Geometry

Example Question #272 : Coordinate Geometry

Example Question #52 : How To Find X Or Y Intercept

Example Question #273 : Coordinate Geometry

Example Question #54 : How To Find X Or Y Intercept

Example Question #274 : Coordinate Geometry

Example Question #275 : Coordinate Geometry

Example Question #276 : Coordinate Geometry

All Intermediate Geometry Resources

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