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Pre-Algebra : Graphing

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Example Questions

Example Question #2 : Graphing Lines

What is the y-intercept of the line y=31x-65 ?

Possible Answers:

(-65,0)

(0,-65)

(0,31)

(31,0)

Correct answer:

(0,-65)

Explanation:

In the slope-intercept form of a line, , the y-intercept is when the line intersects the y-axis.

It does this at .

So we plug in for in our equation

y=31x-65

to give us

y=31(0)-65

Anything multiplied by is so

y=-65

Our coordinates for the y-intercept are (0,-65) .

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Example Question #4 : Graphing Lines

What is the slope of a line that is parallel to y=16x+17 ?

Possible Answers:

m=16

m=17

$m=-\frac{1}{16}$

m=-16

Correct answer:

m=16

Explanation:

Parallel lines have the same slope.

If an equation is in slope-intercept form, , we take the from our equation and set it equal to the slope of our parallel line.

In this case m=16 .

The slope of our parallel line is m=16 .

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Example Question #3 : Graphing Lines

What is the slope of the line that contains the points, (8,16) and (4,8) ?

Possible Answers:

m=4

m=2

m=8

m=16

Correct answer:

m=2

Explanation:

To find the slope of a line with two points you must properly plug the points into the slope equation for two points which looks like

We must then properly assign the points to the equation as and .

In this case we will make (8,16) our and (4,8) our .

Plugging the points into the equation yields

$m=\frac{(16-8)}{(8-4)}$

Perform the math to arrive at

$m=\frac{8}{4}$

The answer is m=2 .

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Example Question #5 : Graphing Lines

What is the slope of the line that contains the points, (1,5) and (2,10) ?

Possible Answers:

m=-5

$m=\frac{1}{5}$

m=5

$m=-\frac{1}{5}$

Correct answer:

m=5

Explanation:

To find the slope of a line with two points you must properly plug the points into the slope equation for two points which looks like

We must then properly assign the points to the equation as and .

In this case we will make (2,10) our , and (1,5) our .

Plugging the points into the equation yields

$m=\frac{10-5}{2-1}$

Perform the math to arrive at

$m=\frac{5}{1}$

The answer is m=5 .

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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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Pre-Algebra : Graphing

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #2 : Graphing Lines

Example Question #4 : Graphing Lines

Example Question #3 : Graphing Lines

Example Question #5 : Graphing Lines

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

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