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Algebra 1 : Equations of Lines

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Example Questions

Example Question #27 : How To Find The Equation Of A Line

Which is the correct equation for this line?

Graph eq 1

Possible Answers:

y=-x+5

$y=\frac{1}{5}x+1$

y=5x+1

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

Correct answer:

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

Explanation:

The equation for a line takes the form y=mx+b where m is the slope and b is the y-intercept, where the graph hits the y-axis.

The y-intercept of this line is 1, so b=1.

We can figure out the slope by comparing how far the line goes up vs. how far it goes over between any 2 points. The two most obvious points on the graph are at (0,1) and (5,0) . Between these two points, the graph moves down 1 and over 5. This means the slope is $\frac{-1}{5}$ , so we'll put that in for m.

The equation is then $y=-\frac{1}{5}x +1$ .

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Example Question #28 : How To Find The Equation Of A Line

Which is the correct equation for this line?

Graph eq 2

Possible Answers:

$y=\frac{3}{5}x-4$

$y=\frac{4}{5}x+6.7$

y=-4x+6.5

$y=-\frac{3}{5}x-4$

Correct answer:

$y=\frac{3}{5}x-4$

Explanation:

The equation for a line takes the form y=mx+b where m is the slope and b is the y-intercept, where the graph hits the y-axis.

The y-intercept of this line is -4, so b=-4.

We can figure out the slope by comparing how far the line goes up vs. how far it goes over between any 2 points. The two most obvious points on the graph are at (0,-4) and (5,-1) . Between these two points, the graph moves up 3 and over 5. This means the slope is $\frac{3}{5}$ , so we'll put that in for m.

The equation is then $y=\frac{3}{5}x -4$ .

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Example Question #31 : How To Find The Equation Of A Line

Find the equation of the line in the form

y=mx+b

with m=2 through the point (2,3) .

Possible Answers:

y=2x+3

y=3x+2

y=2x-1

y=3x-1

y=2x-4

Correct answer:

y=2x-1

Explanation:

We are given the slope and a point, which we will plug into y=mx+b .

(3)=(2)(2)+b

3=4+b

-1=b .

Thus, using the given and the you just found, the equation of our line is:

y=2x-1

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Example Question #31 : Slope And Line Equations

$\small (4,2) (5,6)$ $\small y-intercept = 4$

Using the data provided, find the equation of the line.

Possible Answers:

$\small y = 3x -1$

$\small y = 6x + 21$

$\small y = {4}x + 4$

$\small y = \frac{3}{2}x + 5$

$\small y = 4x + 5$

Correct answer:

$\small y = {4}x + 4$

Explanation:

The equation for a line is always $\small y = mx + b$ , where $\small m = slope$ and $\small b = y-intercept$ .

Given two data points, we are able to find the slope, m, using the formula

$\small \frac{y_{1}-y_{2}}{x_{1}-x_{2}}$ .

Using the data points provided, our formula will be:

$\small \frac{6-2}{5-4}$ , which gives us $\small \frac{4}{1}=4$ or , $\small m = 4$ .

Our y-intercept is given.

Thus our equation for the line containing these points and that y-intercept is $\small y = {4}x + 4$ .

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Example Question #31 : How To Find The Equation Of A Line

Find the equation of a line given the points $\small (8,3) (2,1) y - intercept = 3$ .

Possible Answers:

$\small y = \frac{2}{6}x +7$

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

$\small y = \frac{3}{6}x +5$

$\small y = \frac{1}{6}x +3$

Correct answer:

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

Explanation:

The equation of a line is $\small y=mx+b$ , where "m" is the slope of the line and "b" is the point at which the line intercepts the y-axis.

The first thing we must do is use the formula

$\frac{y_{1}-y_{2}}{x_{1}-x_{2}}{}$

to find the slope, or "m."

If we plug in the points of the two coordinates given,

$\small \frac{3-1}{8-2} = \frac{2}{6}=\frac{1}{3}$ ,

we find our slope, "m."

Since our y-intercept is given, we now have everything we need for our equation,

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

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Example Question #34 : How To Find The Equation Of A Line

Find the equation for the line given these two points:

$\small (10,2)(9,1) , y-intercept = 0$

Possible Answers:

$\small y = \frac {1}{2}x$

$\small y =3x$

$\small \small y=x$

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

Correct answer:

$\small \small y=x$

Explanation:

The equation of a line is $\small y=mx+b$ , where "m" is the slope of the line and "b" is the point at which the line intercepts the y-axis.

The first thing we must do is use the formula

${} \frac{y_{1}-y_{2}}{x_{1}-x_{2}}$

to find the slope, or "m."

If we plug in the points of the two coordinates given,

$\small \small \frac{2-1}{10-9} = \frac{1}{1} = 1$ , we find our slope, "m."

Since our y-intercept is given, we now have everything we need for our equation, $\small \small y=x$ .

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Example Question #33 : How To Find The Equation Of A Line

Find the equation of the line containing the points:

$\small (9,10) (3,6) , y-intercept = -3$

Possible Answers:

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

$\small \small y=\frac{4}{6}x -10$

$\small \small \small y=\frac{5}{6}x -5$

$\small \small \small y=\frac{4}{6}x -6$

Correct answer:

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

Explanation:

The equation of a line is $\small y=mx+b$ , where "m" is the slope of the line and "b" is the point at which the line intercepts the y-axis.

The first thing we must do is use the formula

${} \frac{y_{1}-y_{2}}{x_{1}-x_{2}}$ to find the slope, or "m."

If we plug in the points of the two coordinates given,

$\small \small \frac{10-6}{9-3} = \frac{4}{6}=\frac{2}{3}$ ,

we find our slope, "m."

Since our y-intercept is given, we now have everything we need for our equation,

$\small \small \small y=\frac{2}{3}x -3$ .

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Example Question #34 : How To Find The Equation Of A Line

Find the equation of the lines given the points:

$\small (30,4)(16, -9) , y-intercept = -6$

Possible Answers:

$\small y=\frac{13}{14}x -6$

$\small y=\frac{13}{14}x -100$

$\small y=-\frac{14}{13}x -4$

$\small y=\frac{13}{14}x -9$

$\small y=-\frac{13}{14}x -6$

Correct answer:

$\small y=\frac{13}{14}x -6$

Explanation:

The equation of a line is $\small y=mx+b$ , where "m" is the slope of the line and "b" is the point at which the line intercepts the y-axis.

The first thing we must do is use the formula

$\frac{y_{1}-y_{2}}{x_{1}-x_{2}}{}$

to find the slope, or "m."

If we plug in the points of the two coordinates given,

$\small \small \small \frac{4--9}{30-16} = \frac{13}{14}$ ,

we find our slope, "m."

Since our y-intercept is given, we now have everything we need for our equation,

$\small \small \small \small \small y=\frac{13}{14}x -6$ .

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Example Question #35 : How To Find The Equation Of A Line

$\small \small (3,1)(8,3), y-intercept = 4$

Using the data above, find the equation of the line.

Possible Answers:

$\small y = \frac{4}{5}x+2$

$\small y = \frac{2}{5}x+10$

$\small y = \frac{2}{5}x+4$

$\small y = \frac{2}{5}x+9$

Correct answer:

$\small y = \frac{2}{5}x+4$

Explanation:

The data provided is enough data to for us to find the equation of a line that passes through these points:

$\small \small (3,1)(8,3), y-intercept = 4$ .

An equation representing a line:

$\small y=mx+b$ ,

where m = slope, b = y-intercept.

To find the slope use the following formula,

$\small \frac{y_{2}-y_{1}}{x_{2}-x_{2}}$ ,

so in this problem the slope:

$\small \small \frac{3-1}{8-3} = \frac{2}{5}$ .

The y-intercept is given. So our equation is

$\small \small y = \frac{2}{5}x+4$ .

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Example Question #36 : How To Find The Equation Of A Line

Given this information, find the equation of the line. "This line passes through two points, one of which is $\small (6,6)$ and the other is $\small (-4,-7)$ . The line also passes through the origin.

Possible Answers:

$\small y = \frac{13}{1}x+1$

$\small y = -\frac{13}{10}x+0$

$\small y = \frac{13}{10}x+10$

$\small y = \frac{13}{10}x$

Correct answer:

$\small y = \frac{13}{10}x$

Explanation:

The data provided is enough data to for us to find the equation of a line that passes through these points:

$\small \small \small (6,6)(-4,-7), y-intercept = 0$ .

An equation representing a line:

$\small y=mx+b$ ,

where m = slope, b = y-intercept.

To find the slope use the following formula,

$\small \frac{y_{2}-y_{1}}{x_{2}-x_{2}}$ ,

so in this problem the slope:

$\small \small \small \frac{6--7}{6--4} = \frac{13}{10}$ .

The y-intercept is given. So our equation is

$\small \small \small y = \frac{13}{10}x$ .

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Algebra 1 : Equations of Lines

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #27 : How To Find The Equation Of A Line

Example Question #28 : How To Find The Equation Of A Line

Example Question #31 : How To Find The Equation Of A Line

Example Question #31 : Slope And Line Equations

Example Question #31 : How To Find The Equation Of A Line

Example Question #34 : How To Find The Equation Of A Line

Example Question #33 : How To Find The Equation Of A Line

Example Question #34 : How To Find The Equation Of A Line

Example Question #35 : How To Find The Equation Of A Line

Example Question #36 : How To Find The Equation Of A Line

All Algebra 1 Resources

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