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Algebra 1 : Slope and Line Equations

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Example Questions

Example Question #41 : How To Find The Equation Of A Line

Given the points (3,2) and (6,4) .

Find the slope-intercept form of the line that contains these points.

Possible Answers:

$y=\frac{2}{3}x-4$

$y=\frac{5}{2}x-\frac{9}{2}$

$y=\frac{3}{2}x-9$

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

$y=\frac{3}{4}x+\frac{9}{2}$

Correct answer:

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

Explanation:

Use the given points and plug them into slope formula:

$m=\frac{\left ( y_{2}-y_{1} \right )}{(x_{2}-x_{1})}$

Remember points are written in the following format:

(x,y)

Substitute.

$m=\frac{4-2}{6-3}$

$m=\frac{2}{3}$

Now, that we have the slope of the line we can insert values into the point-slope formula:

$(y-y_{1})=m(x-x_{1})$

$(y-2)=\frac{2}{3}(x-3)$

Distribute the fraction through the quantity on the left side of the equation.

$(y-2)= \left (\frac{2}{3}*\frac{x}{1} \right ) - \left ( \frac{3}{1} *\frac{2}{3}\right )$

$(y-2)= \left (\frac{2}{3}x\right ) - \left ( \frac{2}{1}\right )$

$y-2= \left (\frac{2}{3}x\right ) - 2$

Add to both sides.

$y= \left (\frac{2}{3}x\right )$

The slope-intercept form is written as:

y=mx+b

Where is the slope and is the y-intercept.

In our equation our slope is $\frac{2}{3}$ and our y-intercept is .

The equation of the line that contains these points is:

$y=\frac{2}{3}x+0$

Simplify.

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

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Example Question #41 : Slope And Line Equations

Write the slope-intercept form of the equation of the line described.

Passes through the point (3,1) , perpendicular to $y=-\frac{2}5{}x-3$ .

Possible Answers:

$y=-\frac{2}{5}x+\frac{11}{5}$

$y=\frac{5}{2}x-\frac{13}{2}$

$y=-\frac{5}{2}x+\frac{17}{2}$

$y=-\frac{2}5{}x+\frac{13}{5}$

$y=-\frac{1}{2}x+\frac{11}{5}$

Correct answer:

$y=\frac{5}{2}x-\frac{13}{2}$

Explanation:

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

A line that is perpendicular has a slope that is the opposite reciprocal of the given line.

Slope of perpendicular line:

$m=\frac{5}{2}$

Using the point slope formula,

$y-y_{1}=m(x-x_{1})$

where $x_{1}=3\: \:and\: \:y_{1}=1$

we get the following equation.

$y-1=\frac{5}{2}(x-3)$

$y=\frac{5}{2}x-\frac{15}{2}+1$

$y=\frac{5}{2}x-\frac{13}{2}$

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Example Question #41 : How To Find The Equation Of A Line

Find the equation of the line with a slope of 2 that passes through the point (4,6).

Possible Answers:

y=2x+2

y=2x+4

y=2x-2

y=2x-14

Correct answer:

y=2x-2

Explanation:

To solve this problem, we need to remember point-slope formula:

$y-y_{1}=m(x-x_{1})$

Then we plug in m=2 and (x1,y1)=(4,6) and solve:

y-6=2(x-4)

y-6=2x-8

y=2x-2

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Example Question #42 : How To Find The Equation Of A Line

Find the equation of the line with slope 1/3 running through the point (15,2).

Possible Answers:

y=3x+15

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

y=3x-2

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

Correct answer:

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

Explanation:

To solve this problem, we need to remember point-slope formula:

$y-y_{1}=m(x-x_{1})$

Then we plug in m=1/3 and (x1,y1)=(15,2) and solve:

$y-2=\frac{1}{3}(x-15)$

$y-2=\frac{1}{3}x-5$

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

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Example Question #43 : How To Find The Equation Of A Line

Find the equation of the line with slope 4 running through the point (-1,-5).

Possible Answers:

y=8x-4

y=2x+5

y=4x-1

y=4x+1

Correct answer:

y=4x-1

Explanation:

To solve this problem, we need to remember point-slope formula:

$y-y_{1}=m(x-x_{1})$

Then we plug in m=4 and (x1,y1)=(-1,-5) and solve:

y-(-5)=4(x-(-1))

y+5=4(x+1)

y+5=4x+4

y=4x-1

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Example Question #43 : How To Find The Equation Of A Line

Find the equation of the line with slope -3 running through the point (2,5).

Possible Answers:

y=-3x+5

y=3x+11

y=-3x+1

y=-3x+11

Correct answer:

y=-3x+11

Explanation:

To solve this problem, we need to remember point-slope formula:

$y-y_{1}=m(x-x_{1})$

Then we plug in m=2 and (x1,y1)=(4,6) and solve:

y-5=-3(x-2)

y-5=-3x+6

y=-3x+11

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Example Question #44 : How To Find The Equation Of A Line

Find the equation of the line with slope -1 running through the point (2,-2).

Possible Answers:

y=-x

y=-x+1

y=-x+2

y=x-2

Correct answer:

y=-x

Explanation:

To solve this problem, we need to remember point-slope formula:

$y-y_{1}=m(x-x_{1})$

Then we plug in m=-1 and (x1,y1)=(2,-2) and solve:

y-(-2)=-1(x-2)

y+2=-1x+2

y=-x

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Example Question #45 : Slope And Line Equations

Find the equation of the line with slope 1/2 running through the point (-8,2).

Possible Answers:

y=2x+6

$y=\frac{1}{2}x-4$

$y=\frac{1}{2}x-6$

$y=\frac{1}{2}x+6$

Correct answer:

$y=\frac{1}{2}x+6$

Explanation:

To solve this problem, we need to remember point-slope formula:

$y-y_{1}=m(x-x_{1})$

Then we plug in m=1/2 and (x1,y1)=(-8,2) and solve:

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

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

$y-2=\frac{1}{2}x+4$

$y=\frac{1}{2}x+6$

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Example Question #45 : How To Find The Equation Of A Line

Find the equation of the line with slope -2 running through the point (1,3).

Possible Answers:

y=-2x+5

y=-2x-5

y=2x+5

y=2x-5

Correct answer:

y=-2x+5

Explanation:

To solve this problem, we need to remember point-slope formula:

$y-y_{1}=m(x-x_{1})$

Then we plug in m=-2 and (x1,y1)=(1,3) and solve:

y-3=-2(x-1)

y-3=-2x+2

y=-2x+5

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Example Question #47 : Slope And Line Equations

Find the equation of the line with the slope 1/4 running through the point (2,2).

Possible Answers:

$y=4x+\frac{3}{2}$

y=4x+2

$y=\frac{1}{4}x+3$

$y=\frac{1}{4}x+\frac{3}{2}$

Correct answer:

$y=\frac{1}{4}x+\frac{3}{2}$

Explanation:

To solve this problem, we need to remember point-slope formula:

$y-y_{1}=m(x-x_{1})$

Then we plug in m=1/4 and (x1,y1)=(2,2) and solve:

$y-2=\frac{1}{4}(x-2)$

$y-2=\frac{1}{4}x-\frac{2}{4}$

$y=\frac{1}{4}x-\frac{1}{2}+2$

$y=\frac{1}{4}x+\frac{3}{2}$

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Algebra 1 : Slope and Line Equations

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #41 : How To Find The Equation Of A Line

Example Question #41 : Slope And Line Equations

Example Question #41 : How To Find The Equation Of A Line

Example Question #42 : How To Find The Equation Of A Line

Example Question #43 : How To Find The Equation Of A Line

Example Question #43 : How To Find The Equation Of A Line

Example Question #44 : How To Find The Equation Of A Line

Example Question #45 : Slope And Line Equations

Example Question #45 : How To Find The Equation Of A Line

Example Question #47 : Slope And Line Equations

All Algebra 1 Resources

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