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Algebra 1 : Slope and Line Equations

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Example Question #11 :How To Find The Equation Of A Line

Which of these lines has a slope ofand a-intercept of?

Possible Answers:

y=4x+6

y=4x-6

y=2x-3

None of the other answers

y=-6x+4

Correct answer:

y=4x-6

Explanation:

When a line is in the y=mx+b form, theis its slope and theis its-intercept. Thus, the only line with a slope ofand a-intercept ofis

y=4x-6 .

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Example Question #3631 :Algebra 1

What is the equation of a line with a slope of 3 that runs through the point (4,9)?

Possible Answers:

None of the other answers

y=-3x-3

y=3x-3

y=3x+3

y=-3x+3

Correct answer:

y=3x-3

Explanation:

You can find the equation by plugging in all of the information to the y=mx+b formula.

The slope (or) is 3. So, the equation is now y=3x+b .

You are also given a point on the line: (4,9), which you can plug into the equation:

9=3(4)+b

Solve forto get b=-3 .

Now that you have theand, you can determine that the equation of the line is y=3x-3 .

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Example Question #13 :How To Find The Equation Of A Line

What is the equation of the line passing through the points (1,2) and (3,1) ?

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

First find the slope of the 2 points:

$\frac{1-2}{3-1}=\frac{-1}{2}$

Then use the slope and one of the points to find the y-intercept:

$2=\frac{-1}{2}(1)+b$

$\frac{4}{2}+\frac{1}{2}=-\frac{1}{2}+\frac{1}{2}+b$

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

So the final equation is $y=-\frac{1}{2}x+\frac{5}{2}$

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Example Question #14 :How To Find The Equation Of A Line

What is the slope and y-intercept of 2y-4x=12 ?

Possible Answers:

Slope:; y-intercept:

None of the other answers

Slope:; y-intercept:

Correct answer:

Slope:; y-intercept:

Explanation:

The easiest way to determine the slope and y-intercept of a line is by rearranging its equation to the y=mx+b form. In this form, the slope is theand the y-intercept is the.

Rearranging 2y-4x=12

gives you

y=2x+6

which has anof 2 and aof 6.

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Example Question #11 :How To Find The Equation Of A Line

Find the equation of the line, in y=mx+b form, that contains the points (1,6) , (11,12) , and (-9,0) .

Possible Answers:

$y = \frac{3}{5}x - 7$

y = 10x - 4

y = 3x +5

$y = \frac{5}{3}x + \frac{13}{3}$

$y=\frac{3}{5}x +\frac{27}{5}$

Correct answer:

$y=\frac{3}{5}x +\frac{27}{5}$

Explanation:

When finding the equation of a line given two or more points, the first step is to find the slope of that line. We can use the slope equation, $\frac{y_{2}-y_{_{1}}}{x_{2}-x_{1}}$ . Any combination of the three points can be used, but let's consider the first two points, (1,6) and (11,12) .

$\frac{12-6}{11-1} = \frac{3}{5}$

So $\frac{3}{5}$ is our slope.

Now, we have the half-finished equation

$y = \frac{3}{5}x + b$

and we can complete it by plugging in theandvalues of any point. Let's use (1,6) .

Solving

$6 = \frac{3}{5}(1)+b$

forgives us

$b = 6 - \frac{3}{5}$

$b = 5\frac{2}{5} = \frac{27}{5}$

We now have our completed equation:

$y = \frac{3}{5}x + \frac{27}{5}$

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Example Question #16 :How To Find The Equation Of A Line

We have two points: (-3,-1) and (4,9) .

If these two points are connected by a straight line, find the equation describing this straight line.

Possible Answers:

None of these

$y=\frac{10}{7}x+\frac{23}{7}$

$y=-\frac{10}{3}x+\frac{3}{7}$

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

$y=\frac{10}{3}x+\frac{3}{7}$

Correct answer:

$y=\frac{10}{7}x+\frac{23}{7}$

Explanation:

We need to find the equation of the line in slope-intercept form.

y=mx+b

In this formula,is equal to the slope andis equal to the y-intercept.

To find this equation, first, we need to find the slope by using the formula for the slope between two point.

$m=\frac{y_2-y_1}{x_2-x_1}$

In the formula, the points areand. In our case, the points are (-3,-1) and (4,9) . Using our values allows us to solve for the slope.

$m=\frac{9-(-1)}{4-(-3)}=\frac{10}{7}$

We can replace the variablewith our new slope.

$y=\frac{10}{7}x+b$

Next, we need to find the y-intercept. To find this intercept, we can pick one of our given points and use it in the formula.

(-3,-1)

$-1=\frac{10}{7}(-3)+b$

Solve for.

$-1=\frac{-30}{7}+b$

$b=-1+\frac{30}{7}$

$b=\frac{23}{7}$

Now, the final equation connecting the two points can be written using the new value for the y-intercept.

$y=\frac{10}{7}x+\frac{23}{7}$

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Example Question #17 :How To Find The Equation Of A Line

Which of these lines has a slope ofand a y-intercept of?

Possible Answers:

None of the other answers

y=-3x+4

y=-4x+3

y=4x-3

y=3x-4

Correct answer:

y=-3x+4

Explanation:

Since all of the answers are in the y=mx+b form, the slope of each line is indicated by itsand its y-intercept is indicated by its. Thus, a line with a slope ofand a y-intercept ofmust have an equation of y=-3x+4 .

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Example Question #18 :How To Find The Equation Of A Line

Find the domain of:

$\sqrt{2x-5}$

Possible Answers:

$\left \{ x|x\leq \frac{5}{2} \right \}$

$\left \{ x|x= \frac{5}{2} \right \}$

$\left \{ x|x\neq \frac{5}{2} \right \}$

$\left \{ x|-\infty < x< \infty \right \}$

$\left \{ x|x\geq \frac{5}{2} \right \}$

Correct answer:

$\left \{ x|x\geq \frac{5}{2} \right \}$

Explanation:

The expression under the radical must be $\geq 0$ . Hence

$\sqrt{2x-5} \geq 0$

Solving for, we get

$x\geq \frac{5}{2}$

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Example Question #19 :How To Find The Equation Of A Line

Give, in slope-intercept form, the equation of a line through the points (-2, 5) and (-3, 8) .

Possible Answers:

y = -3x -1

y = -3x +5

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

y = -3x -7

$y = -\frac{1}{3}x +8$

Correct answer:

y = -3x -1

Explanation:

First, use the slope formula to find the slope, setting $x_{1} = -2, y_{1} = 5,x_{2} = -3, y_{2} = 8$ .

$m = \frac{y _{2} - y_{1}}{x _{2} - x_{1}} = \frac{8 -5 }{-3-(-2)} = \frac{3 }{-1} = -3$

We can write the equation in slope-intercept form as

y = mx + b .

Replace m = -3 :

y = -3x + b

We can findby substituting for x,y using either point - we will choose (-2, 5) :

5= -3 (-2) + b

5= 6 + b

5-6 = 6 -6 + b

b = -1

The equation is y = -3x -1 .

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Example Question #11 :Slope And Line Equations

Give, in slope-intercept form, the equation of a line through the points $\left (3.5, 5.5 \right )$ and (5.5, -2.5) .

Possible Answers:

y = -0.25x + 5.5

y = -4x + 3.5

y = -4x + 19.5

y = -0.25x + 13.5

y = -4x + 2.5

Correct answer:

y = -4x + 19.5

Explanation:

First, use the slope formula to find the slope, setting $x_{1} = 3.5, y_{1} = 5.5,x_{2} = 5.5, y_{2} = -2.5$ .

$m = \frac{y _{2} - y_{1}}{x _{2} - x_{1}} = \frac{-2.5 -5.5}{5.5-3.5} = \frac{-8 }{2} = -4$

We can write the equation in slope-intercept form as

y = mx + b .

Replace m = -4 :

y = -4x + b

We can findby substituting for x,y using either point - we will choose (3.5, 5.5) :

5.5= -4 (3.5) + b

5.5= -14 +b

5.5+14 = -14 +14+b

b = 19.5

The equation is y = -4x + 19.5 .

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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 #11 :How To Find The Equation Of A Line

Example Question #3631 :Algebra 1

Example Question #13 :How To Find The Equation Of A Line

Example Question #14 :How To Find The Equation Of A Line

Example Question #11 :How To Find The Equation Of A Line

Example Question #16 :How To Find The Equation Of A Line

Example Question #17 :How To Find The Equation Of A Line

Example Question #18 :How To Find The Equation Of A Line

Example Question #19 :How To Find The Equation Of A Line

Example Question #11 :Slope And Line Equations

All Algebra 1 Resources

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