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Intermediate Geometry : Intermediate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

Example Question #1521 : Intermediate Geometry

Find the y-intercept for the line

4x - 3y + 24 = 0 .

Possible Answers:

(0,6)

(0,0)

(0,8)

(0,-6)

(0,-8)

Correct answer:

(0,8)

Explanation:

To find the y-intercept, plug in 0 for x, since the y-axis is where x = 0.

4(0) - 3y + 24 = 0

0 - 3y + 24 = 0 subtract 24 from both sides

-3y = -24 divide by -3

y = 8

The y-intercept is (0,8)

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Example Question #11 : How To Find X Or Y Intercept

Find the x-intercept for the line

$y = -\frac{1}{3} x + 5$ .

Possible Answers:

(-5,0)

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

(15,0)

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

(5,0)

Correct answer:

(15,0)

Explanation:

To find the x-intercept, plug in 0 for y, since the x-axis is where y = 0

$0 = -\frac{1}{3} x + 5$ subtract 5 from both sides

$-5 = -\frac{1}{3}x$ multiply both sides by -3

15 = x

The x-intercept is (15, 0 )

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Example Question #231 : Coordinate Geometry

What is the y intercept of the line :

y-2 = 2(x -4)

Possible Answers:

y=6

y=-8

y=3

y= -6

y=-10

Correct answer:

y= -6

Explanation:

Here all we have to remember is that when given a linear equation to find the y-intercept, or where the line crosses the y-axis, we just need to set x=0 and solve for y. This solution is shown below:

$y-2 =2(x-4) \rightarrow \text{set} \; x=0 \rightarrow y-2 =2(-4) \newline \rightarrow y-2=-8 \rightarrow \text{now add 2 to each side} \rightarrow y=-6$

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Example Question #16 : X And Y Intercept

A rocket is fired that follows the below parabolic path where h(t) represents the height (in feet) over time (in seconds). How much time did the rocket spend in the air?

$h(t)=256t-16t^{2}$

Possible Answers:

8 seconds

256 seconds

16 seconds

0 seconds

Correct answer:

16 seconds

Explanation:

To solve, you must find the zeros or x-intercepts for the function h(t).

To find x-intercepts, we must plug in 0 for h(t).

$h(t)=256t-16t^{2}$

$0=256t-16t^{2}$

Factor to solve - divide by 16t.

0=16t(16-t)

Set both parts equat to zero.

16t=0 16-t=0

$t = 0\ and\ t=16$

The answer is t=16 because when t=0, that is when the rocket is first being fired from the ground, the rocket then returns to the ground after having spent 16 seconds in the air.

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Example Question #17 : X And Y Intercept

Find the y-intercept(s) for the circle given by the equation below:

$(x-5)^{2}+(y+2)^{2}=25$

Possible Answers:

Correct answer:

Explanation:

To find the y-intercept for any equation, plug in 0 for x in the original equation.

$(0-5)^{2}+(y+2)^{2}=25$

Simplify

$25+(y+2)^{2}=25$

Subtract 25 from both sides

$(y+2)^{2}=0$

Take the square root of both sides

y+2=0

Subtract 2 from both sides to get the y-intercept.

y=-2

This circle has one y-intercept.

It is possible for a circle to have one y-intercept, two y-intercepts or no y-intercepts.

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Example Question #18 : X And Y Intercept

Find the x-intercept(s) for the circle defined by (x+1)^2 + (y-3)^2 = 25

Possible Answers:

x = 3

x = 7

x= 5, -3

x = 5

x=3, -5

Correct answer:

x=3, -5

Explanation:

The x-intercepts occur when y is equal to zero. So to figure out the x-intercepts, plug in 0 for y:

(x+1)^2 + (0-3)^2 = 25

(x+1)^2 + 9 = 25 subtract 9 from both sides

(x+1)^2 = 16 take the square root of both sides

x + 1 = 4, -4 there are 2 possibilities here since 4^2 = 16 and also (-4)^2 = 16

One solution: x + 1 = 4 subtract 1 from both sides

x = 3

The other solution: x + 1 = -4 subtract 1 from both sides

x = -5

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Example Question #241 : Coordinate Geometry

Find the y-intercept(s) for the equation y = |x - 3|

Possible Answers:

y = 3, -3

y = 3, 6

y = 0, 6

y = -3

y = 3

Correct answer:

y = 3

Explanation:

The y-intercept occurs when x is 0, so plug in 0 for x:

y = | 0 - 3| = | -3| = 3

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Example Question #20 : X And Y Intercept

Find the x- and y-intercepts for the equation y =-2x+ 5

Possible Answers:

(2.5, 0); (0,5)

(10, 0 ) ; (5, 0 )

(10, 0 ) ; (0 , -5)

(-2.5, 0 ) ; (0, 5)

(0, 2.5); (5, 0 )

Correct answer:

(2.5, 0); (0,5)

Explanation:

To find the x-intercept, plug in 0 for y:

0 = -2x+ 5 subtract 5 from both sides

-5 = -2x divide both sides by -2

2.5 = x since x is 2.5 and y is 0, this point is (2.5, 0 )

To find the y-intercept, plug in 0 for x:

y = -2(0)+ 5

y = 0 + 5 = 5

This gives the point (0,5)

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

Find the -intercept for the line 2x-y=12 .

Possible Answers:

(6, 0)

(-6, 0)

(0, 6)

(0, -6)

Correct answer:

(6, 0)

Explanation:

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

2x-y=12

y+12=2x

y=2x-12

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.

2x-12=0

Now, solve for .

2x=12

x=6

The x-intercept is found at (6, 0) .

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Example Question #1522 : Intermediate Geometry

Find the x-intercept for the line 12x-9y=4 .

Possible Answers:

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

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

$(\frac{1}{3}, 0)$

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

Correct answer:

$(\frac{1}{3}, 0)$

Explanation:

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

12x-9y=4

9y+4=12x

9y=12x-4

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

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.

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

Now, solve for .

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

$x=\frac{1}{3}$

The x-intercept is found at $(\frac{1}{3}, 0)$ .

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Intermediate Geometry : Intermediate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #1521 : Intermediate Geometry

Example Question #11 : How To Find X Or Y Intercept

Example Question #231 : Coordinate Geometry

Example Question #16 : X And Y Intercept

Example Question #17 : X And Y Intercept

Example Question #18 : X And Y Intercept

Example Question #241 : Coordinate Geometry

Example Question #20 : X And Y Intercept

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

Example Question #1522 : Intermediate Geometry

All Intermediate Geometry Resources

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