Pre-Algebra Examples

$(5, 8)$ , $(6, 12)$

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.

$m = \frac{12 - (8)}{6 - (5)}$

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 $8$ .

$m = \frac{12 - 8}{6 - (5)}$

Step 1.4.1.2

Subtract $8$ from $12$ .

$m = \frac{4}{6 - (5)}$

Step 1.4.2

Simplify the denominator.

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Step 1.4.2.1

Multiply $- 1$ by $5$ .

$m = \frac{4}{6 - 5}$

Step 1.4.2.2

Subtract $5$ from $6$ .

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

Step 1.4.3

Divide $4$ by $1$ .

$m = 4$

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, $y = m x + b$ .

$y = (4) \cdot x + b$

Step 2.2

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

$y = (4) \cdot (5) + b$

Step 2.3

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

$8 = (4) \cdot (5) + b$

Step 2.4

Rewrite the equation as $(4) \cdot (5) + b = 8$ .

$(4) \cdot (5) + b = 8$

Step 2.5

Multiply $4$ by $5$ .

$20 + b = 8$

Step 2.6

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

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Step 2.6.1

Subtract $20$ from both sides of the equation.

$b = 8 - 20$

Step 2.6.2

Subtract $20$ from $8$ .

$b = - 12$

Step 3

List the slope and y-intercept.

Slope: $4$

y-intercept: $(0, - 12)$

Step 4