Pre-Algebra Examples

$(- 4, 1)$ , $(3, 7)$

Step 1

Find the value of the slope.

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Step 1.1

Slope is equal to the change in $y$ over the change in $x$ , or rise over run.

$m = \frac{change in y}{change in x}$

Step 1.2

The change in $x$ is equal to the difference in x-coordinates (also called run), and the change in $y$ is equal to the difference in y-coordinates (also called rise).

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

Step 1.3

Substitute in the values of $x$ and $y$ into the equation to find the slope.

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

Step 1.4

Simplify.

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Step 1.4.1

Simplify the numerator.

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Step 1.4.1.1

Multiply $- 1$ by $1$ .

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

Step 1.4.1.2

Subtract $1$ from $7$ .

$m = \frac{6}{3 - (- 4)}$

Step 1.4.2

Simplify the denominator.

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Step 1.4.2.1

Multiply $- 1$ by $- 4$ .

$m = \frac{6}{3 + 4}$

Step 1.4.2.2

Add $3$ and $4$ .

$m = \frac{6}{7}$

Step 2

Find the value of the y-intercept.

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Step 2.1

Substitute the value of $m$ into the slope-intercept form of the equation, $y = m x + b$ .

$y = (\frac{6}{7}) x + b$

Step 2.2

Substitute the value of $x$ into the slope-intercept form of the equation, $y = m x + b$ .

$y = (\frac{6}{7}) \cdot (- 4) + b$

Step 2.3

Substitute the value of $y$ into the slope-intercept form of the equation, $y = m x + b$ .

$1 = (\frac{6}{7}) \cdot (- 4) + b$

Step 2.4

Rewrite the equation as $(\frac{6}{7}) \cdot (- 4) + b = 1$ .

$(\frac{6}{7}) \cdot (- 4) + b = 1$

Step 2.5

Simplify each term.

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Step 2.5.1

Multiply $(\frac{6}{7}) (- 4)$ .

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Step 2.5.1.1

Combine $\frac{6}{7}$ and $- 4$ .

$\frac{6 \cdot - 4}{7} + b = 1$

Step 2.5.1.2

Multiply $6$ by $- 4$ .

$\frac{- 24}{7} + b = 1$

Step 2.5.2

Move the negative in front of the fraction.

$- \frac{24}{7} + b = 1$

Step 2.6

Move all terms not containing $b$ to the right side of the equation.

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Step 2.6.1

Add $\frac{24}{7}$ to both sides of the equation.

$b = 1 + \frac{24}{7}$

Step 2.6.2

Write $1$ as a fraction with a common denominator.

$b = \frac{7}{7} + \frac{24}{7}$

Step 2.6.3

Combine the numerators over the common denominator.

$b = \frac{7 + 24}{7}$

Step 2.6.4

Add $7$ and $24$ .

$b = \frac{31}{7}$

Step 3

List the slope and y-intercept.

Slope: $\frac{6}{7}$

y-intercept: $(0, \frac{31}{7})$

Step 4