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Pre-Algebra : Graphing Lines

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Example Questions

Example Question #41 : Graphing

What is the slope of a line that is perpendicular to y=44x+92 ?

Possible Answers:

m=44

$m=-\frac{1}{44}$

m=92

m=-44

Correct answer:

$m=-\frac{1}{44}$

Explanation:

The slope of a perpendicular lines has the negative reciprocal of the slope of the original line.

If an equation is in slope-intercept form, , we use the from our equation as our original slope.

In this case m=44

First flip the sign m=-44

To find the reciprocal you take the integer and make it a fraction by placing a over it. If it is already a fraction just flip the numerator and denominator.

Do this to make the slope

$m=-\frac{1}{44}$

The slope of the perpendicular line is

$m=-\frac{1}{44}$ .

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Example Question #42 : Graphing

What is the slope of the following line:

2y=3x+4

Possible Answers:

$\frac{2}{3}$

$\frac{3}{4}$

$\frac{3}{2}$

Correct answer:

$\frac{3}{2}$

Explanation:

To be able to identify the slope of a line, we need to get it in the form of

y=mx+b .

To do this we need to change the coefficient of y to be instead of . To do this, divide both sides of the equation by .

$y=\frac{3}{2}x+2$

Now we can tell what the value of m, or the slope, is: $\frac{3}{2}$

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Example Question #43 : Graphing

(3,5) and (4,7) are two points on a line. What is the slope of this line?

Possible Answers:

$\frac{1}{2}$

Correct answer:

Explanation:

The slope of the line is determined by $\frac{rise}{run}$ . In other words, we can use the formula $\frac{y_2-y_1}{x_2-x_1}$ .

Let's choose the coordinate (3,5) to be ( x_1 , y_1 ) and (4,7) to be ( x_2 , y_2 ).

We can now use the formula above:

$\frac{7-5}{4-3}=2$

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Example Question #44 : Graphing

What is the slope of a line containing the points (1,12) and (-7, 8) ?

Possible Answers:

$2\frac{1}{2}$

$\frac{1}{2}$

$3\tfrac{1}{3}$

$\frac{2}{3}$

Correct answer:

$\frac{1}{2}$

Explanation:

The formula to calculate slope between two points in a line is $m=\frac{Y-y}{X-x}$ , for points (X,Y) and (x,y) .

If we pick (1,12) as our (X,Y) and (-7, 8) as our (x,y) , then:

$m = \frac{12-8}{1-(-7)}$
This simplifies to $m=\frac{4}{8}$ , which can be reduced to $m=\frac{1}{2}$

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Example Question #45 : Graphing

What is the slope-intercept form of a line?

Possible Answers:

ax+by=0

y=ax+b

y=bx+m

ax+y=b

y=mx+b

Correct answer:

y=mx+b

Explanation:

The slope-intercept form of a line is y=mx+b .

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Example Question #46 : Graphing

Which of the follow lines is parallel to:

y=14x+7

Possible Answers:

y=14x+9

$y=\frac{1}{14}x+9$

y=-14x+9

$y=\frac{-1}{14}x+9$

Cannot be determined

Correct answer:

y=14x+9

Explanation:

It is known that parallel lines have the same slope and therefore a line that is parallel to:

y=14x+7

MUST have the same slope of .

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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 #1 : 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:

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

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

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

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

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

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:

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

$\textup{y-intercept} = 5$

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

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

$\textup{slope} = -5$

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

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

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

$\textup{slope} = -5$

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

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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Pre-Algebra : Graphing Lines

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #41 : Graphing

Example Question #42 : Graphing

Example Question #43 : Graphing

Example Question #44 : Graphing

Example Question #45 : Graphing

Example Question #46 : Graphing

Cannot be determined

Example Question #51 : Graphing

Example Question #1 : Graphing

Example Question #52 : Graphing

Example Question #53 : Graphing

All Pre-Algebra Resources

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