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Intermediate Geometry : Intermediate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

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8 Diagnostic Tests 250 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #71 : How To Find X Or Y Intercept

Find the y-intercept of the line that has the equation y+15=-7(x-2) .

Possible Answers:

(0, -13)

(0, -19)

(0, -3)

(0, -1)

Correct answer:

(0, -1)

Explanation:

You should recognize that the given equation is in the point-slope form.

In order to find the y-intercept, rearrange the equation into slope-intercept form, y=mx+b .

y+15=-7(x-2)

y+15=-7x+14

y=-7x-1

Since, b=-1 , the y-intercept must be located at (0,-1) .

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Example Question #72 : How To Find X Or Y Intercept

What is the y-intercept of a line that has the equation y-24=-8(x+1) ?

Possible Answers:

(0, 16)

(0, 10)

(0, 8)

(0, 24)

Correct answer:

(0, 16)

Explanation:

You should recognize that the given equation is in the point-slope form.

In order to find the y-intercept, rearrange the equation into slope-intercept form, y=mx+b .

y-24=-8(x+1)

y-24=-8x-8

y=-8x+16

Since, b=16 , the y-intercept must be located at (0,16) .

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Example Question #73 : How To Find X Or Y Intercept

What is the y-intercept of a line that has the equation $y+29=-\frac{1}{4}(x+36)$ ?

Possible Answers:

(0,-38)

(0, 2)

(0, -29)

(0, -18)

Correct answer:

(0,-38)

Explanation:

You should recognize that the given equation is in the point-slope form.

In order to find the y-intercept, rearrange the equation into slope-intercept form, y=mx+b .

$y+29=-\frac{1}{4}(x+36)$

$y+29=-\frac{1}{4}x-9$

$y=-\frac{1}{4}x-38$

Since, b=-38 , the y-intercept must be located at (0,-38) .

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Example Question #72 : How To Find X Or Y Intercept

What is the y-intercept of the line with the equation?

$y-10=-20(x+\frac{1}{4})$

Possible Answers:

(0, 18)

(0, 5)

(0, 24)

(0, 21)

Correct answer:

(0, 5)

Explanation:

You should recognize that the given equation is in the point-slope form.

In order to find the y-intercept, rearrange the equation into slope-intercept form, y=mx+b .

$y-10=-20(x+\frac{1}{4})$

y-10=-20x-5

y=-20x+5

Since, b=5 , the y-intercept must be located at (0,5) .

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Example Question #75 : X And Y Intercept

True or false: The lines of the equations

2x+y = 12

and

x+2y = 12

have the same -intercept.

Possible Answers:

True

False

Correct answer:

False

Explanation:

The -intercept of a line is the point at which it intersects the -axis; its -coordinate at this point is 0, so its -coordinate can be found by substituting 0 for in the equation and solving for . Do this with both equations:

2x+y = 12

$2 \cdot 0 +y = 12$

0+ y = 12

y = 12

The -intercept of the line is at (0, 12) .

x+2y = 12

0+2y = 12

2y = 12

$\frac{2y }{2}= \frac{12}{2}$

y = 6

The -intercept of the line is at (0, 6) .

The two lines have different -intercepts.

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Example Question #75 : How To Find X Or Y Intercept

True or false: the lines of the equations

y = 6

and

x+ y = 6

have the same -intercept.

Possible Answers:

True

False

Correct answer:

True

Explanation:

The -intercept of a line is the point at which it intersects the -axis; its -coordinate at this point is 0.

The -coordinate of the line of the equation

x+ y = 6

can be found by substituting 0 for in the equation and solving for :

0+ y = 6

y=6

The -intercept of this line is at (0,6) .

The line with equation y = b is a horizontal line with its -intercept at (0,b) , so the -intercept line of the equation y=6 has its -intercept at (0,6) as well.

Both lines indeed have the same -intercept.

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Example Question #73 : How To Find X Or Y Intercept

True or false:

The lines of the equations

$y = \frac{2}{5}x+ 117$

and

$y = - \frac{5}{2}x+ 117$

have the same -intercept.

Possible Answers:

True

False

Correct answer:

True

Explanation:

Both equations are given in the slope-intercept form y = mx+b , in which the stand-alone constant is the -coordinate of the -intercept. In both equations, this value is 117, so (0, 117 ) is the -intercept of both equations.

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Example Question #302 : Coordinate Geometry

Find the y-intercept of a line that has a slope of and passes through the point (12, 4) .

Possible Answers:

(0, -14)

(0, -56)

(0, 55)

(0,5)

Correct answer:

(0, -56)

Explanation:

Recall the point-slope form of the equation of a line that has a slope of and passes through the point (x_1, y_1) :

y-y_1=m(x-x_1)

Plug in the given point and the given slope.

y-4=5(x-12)

Rearrange the equation into slope-intercept form.

y-4=5x-60

y=5x-56

The y-intercept for this line is (0, -56) .

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Example Question #81 : X And Y Intercept

Give the -coordinate of the -intercept of the line of the equation

8x + 7y = 43

Possible Answers:

$5\frac{3}{8}$

$-\frac{7}{8}$

$6\frac{1}{7}$

$-1\frac{1}{7}$

Correct answer:

$5\frac{3}{8}$

Explanation:

The -intercept of the graph of a function is the point at which it intersects the -axis. The -coordinate is 0, so the -coordinate can be found by substituting 0 for in the equation and solving for :

8x + 7y = 43

8x + 7 (0) = 43

8x +0= 43

8x = 43

Divide both sides by 8:

$\frac{8x }{8}= \frac{43}{8}$

$x= 5\frac{3}{8}$

The -intercept of the graph is at the point $\left ( 5\frac{3}{8} , 0\right )$ .

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Example Question #82 : X And Y Intercept

Give the -coordinate of the -intercept of the line of the equation

8x + 7y = 43

Possible Answers:

$5\frac{3}{8}$

$6\frac{1}{7}$

$-\frac{7}{8}$

$-1\frac{1}{7}$

Correct answer:

$6\frac{1}{7}$

Explanation:

The -intercept of the graph of a function is the point at which it intersects the -axis. The -coordinate is 0, so the -coordinate can be found by substituting 0 for in the equation and solving for :

8x + 7y = 43

8 (0) + 7y = 43

0+ 7y = 43

7y = 43

Divide both sides by 7:

$\frac{7y }{7}= \frac{43}{7}$

$y = 6\frac{1}{7}$

The -intercept of the graph is at the point $\left (0, 6\frac{1}{7} \right )$ .

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Intermediate Geometry : Intermediate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #71 : How To Find X Or Y Intercept

Example Question #72 : How To Find X Or Y Intercept

Example Question #73 : How To Find X Or Y Intercept

Example Question #72 : How To Find X Or Y Intercept

Example Question #75 : X And Y Intercept

Example Question #75 : How To Find X Or Y Intercept

Example Question #73 : How To Find X Or Y Intercept

Example Question #302 : Coordinate Geometry

Example Question #81 : X And Y Intercept

Example Question #82 : X And Y Intercept

All Intermediate Geometry Resources

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