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Pre-Algebra : Graphing

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Example Questions

Example Question #51 : Graphing

Write an equation in point-slope form for a line parallel to the line $\small y=4x+4\small$

that goes through the point: $\small \small(1,8)$ .

Possible Answers:

$\small y-4=4(x-4)$

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

$\small y-8=4(x-1)$

$\small y-4=4(x-8)$

$\small y-1=4(x-8)$

Correct answer:

$\small y-8=4(x-1)$

Explanation:

You know that point-slope form is: $y-y_{1}=m(x-x_{1})$

and therefore you must look at the slope of your equation given which is $\small 4$ .

From there you just plug in what is given:

$\small 8$ for $y_{1}$ ,

$\small 4$ for $\small m$ ,

and $\small 1$ for $x_{1}$

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Example Question #51 : Graphing

A line graphed on the coordinate plane below. Graph_of_y_-2x_4

Give the equation of the line in slope intercept form.

Possible Answers:

$\dpi{100} \small y=-2x-4$

$\dpi{100} \small y=2x+4$

$\dpi{100} \small y=2x-4$

$\dpi{100} \small y=-2x+4$

$\dpi{100} \small y=-x+4$

Correct answer:

$\dpi{100} \small y=-2x+4$

Explanation:

The slope of the line is $\dpi{100} \small -2$ and the y-intercept is $\dpi{100} \small 4$ .

The equation of the line is $\dpi{100} \small y=-2x+4$ .

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Example Question #52 : Graphing

What is the slope and y-intercept of the equation

$y = \frac{1}{4}x -5\textup{ ?}$

Possible Answers:

$\textup{slope} = -5$

$\textup{y-intercept} = \frac{1}{4}x$

$\textup{slope} = \frac{1}{4}$

$\textup{y-intercept} = 5$

$\textup{slope} = \frac{1}{4}$

$\textup{y-intercept} = -5$

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

$\textup{y-intercept} = -5$

$\textup{slope} = -5$

$\textup{y-intercept} = \frac{1}{4}$

Correct answer:

$\textup{slope} = \frac{1}{4}$

$\textup{y-intercept} = -5$

Explanation:

The slope intercept formula is:

y = mx + b

m = slope

b = y-intercept

y=1/4x-5

m=1/4

b=-5

slope = 1/4

y-intercept = -5

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Example Question #53 : Graphing

What is the slope and y-intercept of the equation below?

$y= -\frac{1}{2}x -8$

Possible Answers:

Slope = $-\frac{1}{2}$

Y-intercept =

Slope = $\frac{1}{2}x$

Y-intercept =

Slope = $-\frac{1}{2}$

Y-intercept =

Slope = $\frac{1}{2}$

Y-intercept =

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

Y-intercept =

Correct answer:

Slope = $-\frac{1}{2}$

Y-intercept =

Explanation:

In order to understand this question you must understand what slope intercept form is.

y= mx + b

= slope

= y-intercept

The slope is $-\frac{1}{2}$

The y-intercept is

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Example Question #21 : Graphing Lines

What is the slope of the line formed by the following equation?

4y=-8x +16

Possible Answers:

Correct answer:

Explanation:

To find the slope of the line, we must write the equation in slope-intercept form or

y =mx+b

where m is the slope and b is the y-intercept.

We must get y by itself. So, we will divide all terms by 4.

4y=-8x +16

$\frac{4y}{4} = \frac{-8x}{4} + \frac{16}{4}$

y = -2x +4

Now that it is in slope-intercept form, we can find the slope. The slope m is the coefficient of the term with the variable x. Therefore, the slope of the line

4y=-8x +16

is -2.

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Example Question #55 : Graphing

Find the line that is parallel to the following line:

y = -3x + 7

Possible Answers:

3y = 2x + 7

y = -2x + 5

y = 3x + 7

-8y = 32x - 4

9y = -27x + 1

Correct answer:

9y = -27x + 1

Explanation:

To find a line that is parallel, we must find a line with the same slope as

y = -3x + 7

When looking at an equation of a line in y-intercept form

y = mx + b

we know m is the slope. So, to determine the slope, we must write the equations in slope-intercept form. Let's look at the equation

9y = -27x + 1

and write it in slope intercept form. We must divide each term by 9.

$\frac{9y}{9} = - \frac{27x}{9} + \frac{1}{9}$

$y = -3x + \frac{1}{9}$

Therefore, the slope of this line is -3. Because it has the same slope as the original equation, this line is parallel to the original line.

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Example Question #22 : Graphing Lines

Find the y-intercept in the following equation:

3y = 9x - 27

Possible Answers:

Correct answer:

Explanation:

To find the y-intercept, we must first write the equation in y-intercept form

y = mx + b

where b is the y-intercept. So,

3y = 9x - 27

we must solve for y. We must divide each term by 3. We get

$\frac{3y}{3} = \frac{9x}{3} - \frac{27}{3}$

y = 3x - 9

Therefore, the y-intercept is -9.

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Example Question #53 : Graphing

What is the slope of the line that contains the points (61,3) and (13,22) ?

Possible Answers:

m=15

$m=-\frac{19}{48}$

$m=\frac{13}{22}$

m=-5

Correct answer:

$m=-\frac{19}{48}$

Explanation:

To find the slope of a line with two points we must properly plug the points into the slope equation:

We must then assign the variables and .

In this case we will plug in (61,3) for and (13,22) for .

Plugging the points into the equation yields $m=\frac{3-13}{61-22}$ .

Perform the math to arrive at $m=\frac{-19}{48}$ .

The answer is $m=-\frac{19}{48}$ .

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Example Question #51 : Graphing

Find the y-intercept of the following equation of a line:

3y = -12x + 36

Possible Answers:

Correct answer:

Explanation:

To find the y-intercept of an equation, we must first write it in slope-intercept form

y = mx +b

where m is the slope and b is the y-intercept. So, in our equation of a line, we must solve for y.

We must divide each term by 3.

$\frac{3y}{3} = \frac{-12x}{3} + \frac{36}{3}$

y = -4x + 12

where -4 is the slope and 12 is the y-intercept.

Therefore, the y-intercept is 12.

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Pre-Algebra : Graphing

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #51 : Graphing

Example Question #51 : Graphing

Example Question #52 : Graphing

Example Question #53 : Graphing

Example Question #21 : Graphing Lines

Example Question #55 : Graphing

Example Question #22 : Graphing Lines

Example Question #53 : Graphing

Example Question #51 : Graphing

All Pre-Algebra Resources

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