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Intermediate Geometry : x and y Intercept

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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 #33 : X And Y Intercept

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

Possible Answers:

(-1, 0)

(-3, 0)

(-6, 0)

(12, 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 #34 : X And Y Intercept

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

Possible Answers:

(7, 0)

(4, 0)

(10, 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 #35 : X And 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 #31 : How To Find X Or Y Intercept

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

Possible Answers:

(13, 0)

(-11, 0)

(24, 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 #37 : X And Y Intercept

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

Possible Answers:

(-61, 0)

(-59, 0)

(-62, 0)

(-60, 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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Example Question #31 : How To Find X Or Y Intercept

Find the y-intercept of the line 16x-20y=200 .

Possible Answers:

(0, 15)

(0, -10)

(0, -20)

(0, 5)

Correct answer:

(0, -10)

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.

16x-20y=200

16(0)-20y=200

-20y=200

y=-10

The y-intercept for this line is (0, -10) .

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Example Question #39 : X And Y Intercept

Find the y-intercept for the line 19x+12y=36 .

Possible Answers:

(0, 6)

(0, 5)

(0, 3)

(0, 2)

Correct answer:

(0, 3)

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.

19x+12y=36

19(0)+12y=36

12y=36

y=3

The y-intercept for this line is (0, 3) .

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Example Question #40 : X And Y Intercept

Find the y-intercept of the line $4x-\frac{1}{3}y=-12$ .

Possible Answers:

(0, 8)

(0, 36)

(0, -4)

(0, -24)

Correct answer:

(0, 36)

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.

$4x-\frac{1}{3}y=-12$

$4(0)-\frac{1}{3}y=-12$

$-\frac{1}{3}y=-12$

y=36

The y-intercept for this line is (0, 36) .

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Intermediate Geometry : x and y Intercept

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #31 : X And Y Intercept

Example Question #32 : X And Y Intercept

Example Question #33 : X And Y Intercept

Example Question #34 : X And Y Intercept

Example Question #35 : X And Y Intercept

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

Example Question #37 : X And Y Intercept

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

Example Question #39 : X And Y Intercept

Example Question #40 : X And Y Intercept

All Intermediate Geometry Resources

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