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Algebra 1 : Equations of Lines

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Example Questions

Example Question #238 : Slope And Line Equations

Find the slope between the following coordinate points:

(12,4) and (6,6)

Possible Answers:

$-\frac{1}{3}$

$\frac{1}{3}$

Correct answer:

$-\frac{1}{3}$

Explanation:

In order to find the slope, we must find the difference in coordinates and divide this number by the difference between the coordinates.

(12,4)(6,6)

$\text{Slope}=\frac{6-4}{6-12}=\frac{2}{-6}=-\frac{1}{3}$

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Example Question #571 : Functions And Lines

Find the slope between the following coordinate points:

(-3,-5) and (-16,8)

Possible Answers:

$\frac{1}{2}$

$-\frac{1}{2}$

Correct answer:

Explanation:

In order to find the slope, we must find the difference in coordinates and divide this number by the difference between the coordinates.

(-3,-5)(-16,8)

$\text{Slope}=\frac{8-(-5)}{-16-(-3)}=\frac{13}{-13}=-1$

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Example Question #572 : Functions And Lines

Find the slope of the equation:

y=5x-9

Possible Answers:

Correct answer:

Explanation:

In order to determine the slope from the given equation we need to make sure that it is written in the following format:

y=mx+b

If the equation of a line is written in the slope-intercept form, then is slope and is the y-intercept.

In this case the slope is:

m=5

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Example Question #171 : How To Find Slope Of A Line

Find the slope of the equation:

2x+3y=10 ?

Possible Answers:

$-\frac{2}{3}$

$-\frac{3}{2}$

$\frac{2}{3}$

Correct answer:

$-\frac{2}{3}$

Explanation:

In order to determine the slope from the given equation we need to make sure that it is written in the following format:

y=mx+b

If the equation of a line is written in the slope-intercept form, then is slope and is the y-intercept.

In this case we need to convert the equation into slope-intercept form.

2x+3y=10

Subtract from both sides.

3y=10-2x

Divide both sides by .

$y=\frac{10-2x}{3}$

Rewrite.

$y=-\frac{2}{3}x+\frac{10}{3}$

Identify the slope.

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

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Example Question #241 : Slope And Line Equations

Find the slope of the equation:

4y+10=x

Possible Answers:

$-\frac{1}{4}$

$\frac{1}{4}$

Correct answer:

$\frac{1}{4}$

Explanation:

In order to determine the slope from the given equation we need to make sure that it is written in the following format:

y=mx+b

If the equation of a line is written in the slope-intercept form, then is slope and is the y-intercept.

In this case we need to convert the equation into slope-intercept form.

4y+10=x

Subtract from both sides.

4y=x-10

Divide both sides by .

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

Identify the slope.

$m=\frac{1}{4}$

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Example Question #242 : Slope And Line Equations

What is the slope of the line connected by the points $(\frac{1}{2},-4)$ and $(4,-\frac{3}{4})$ ?

Possible Answers:

$-\frac{19}{18}$

$\frac{13}{14}$

$-\frac{19}{14}$

$\frac{19}{14}$

$\frac{19}{18}$

Correct answer:

$\frac{13}{14}$

Explanation:

Write the slope formula.

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

Substitute the points into the formula.

$m = \frac{-\frac{3}{4}-(-4)}{4-\frac{1}{2}}$

Rewrite the numbers on the top and bottom with a common denominator.

$m = \frac{-\frac{3}{4}-(-4)}{4-\frac{1}{2}} = \frac{-\frac{3}{4}+\frac{16}{4}}{\frac{8}{2}-\frac{1}{2}}$

Simplify the top and bottom.

$m= \frac{\frac{13}{4}}{\frac{7}{2}}$

Rewrite this complex fraction using multiplication.

$\frac{\frac{13}{4}}{\frac{7}{2}} = \frac{13}{4} \div \frac{7}{2} = \frac{13}{4} \times \frac{2}{7}$

Multiply the numerator by numerator and denominator by denominator.

$\frac{13}{4} \times \frac{2}{7} = \frac{26}{28} = \frac{13}{14}$

The slope is $\frac{13}{14}$ .

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Example Question #582 : Functions And Lines

Find the slope of the line: x+6y = 37

Possible Answers:

$-\frac{1}{6}$

$\frac{1}{6}$

$\frac{37}{6}$

$-\frac{37}{6}$

$-\frac{6}{37}$

Correct answer:

$-\frac{1}{6}$

Explanation:

In order to find the slope, we will need to put this equation in slope-intercept form.

Write the slope-intercept form.

y=mx+b

Isolate the y-term by subtracting on both sides.

x+6y -x= 37-x

Simplify both sides.

6y =-x+37

Divide by six on both sides.

$\frac{6y }{6}=\frac{-x+37}{6}$

Simplify both fractions and split the terms on the right side.

The equation in standard form is: $y=-\frac{1}{6}x+\frac{37}{6}$

We can see that the slope is: $-\frac{1}{6}$

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Example Question #583 : Functions And Lines

Find the slope of the given line:

3x+4=-5y+2

Possible Answers:

$\frac{3}{5} = $ slope$$

$\frac{-3}{5} = $ slope$$

undefined

$\frac{5}{3} = $ slope$$

$\frac{-5}{3} = $ slope$$

Correct answer:

$\frac{-3}{5} = $ slope$$

Explanation:

3x+4=-5y+2

First rearrange in the form y = m*x+b where m = slope and b = y-intercept

(3x+4)-2=(-5y+2)-2

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

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

Slope = $\frac{-3}{5}$

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Example Question #1 : How To Find The Length Of A Line With Distance Formula

Find the length of the line segment from the origin to the point (3, 4).

Possible Answers:

Correct answer:

Explanation:

Here, we need to use the distance formula between the two points (0, 0) and (3, 4).

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$d=\sqrt{(3-0)^2+(4-0)^2}$

$d=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5$

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Example Question #1 : Points And Distance Formula

I have two points, (–8,3) and (6,–1). If I want to connect those two points with a line segment, how long would that line segment need to be?

Possible Answers:

$\frac{5}{2}$

$8\sqrt{2}$

Infinite

$2\sqrt{53}$

Correct answer:

$2\sqrt{53}$

Explanation:

To determine how long the line needs to be to connect those two points, we need to use the distance formula, shown below.

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

The two points are (x_1,y_1) and (x_2,y_2) . In our case, the points are (–8, 3) and (6, –1).

$d=\sqrt{(6-(-8))^2+(-1-3)^2}$

$d=\sqrt{14^2+(-4)^2}$

$d=\sqrt{196+14}$

$d=\sqrt{212}$

$d=\sqrt{4(53)}$

$d=2\sqrt{53}$

So in order to connect the two points, the length of the line needs to have $d=2\sqrt{53}$ .

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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 #238 : Slope And Line Equations

Example Question #571 : Functions And Lines

Example Question #572 : Functions And Lines

Example Question #171 : How To Find Slope Of A Line

Example Question #241 : Slope And Line Equations

Example Question #242 : Slope And Line Equations

Example Question #582 : Functions And Lines

Example Question #583 : Functions And Lines

Example Question #1 : How To Find The Length Of A Line With Distance Formula

Example Question #1 : Points And Distance Formula

All Algebra 1 Resources

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