Pre-Algebra Examples

$(- 2, - 2)$ , $(6, 6)$

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.

$m = \frac{6 - (- 2)}{6 - (- 2)}$

Step 1.4

Cancel the common factor of $6 - (- 2)$ .

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Step 1.4.1

Cancel the common factor.

$m = \frac{6 - (- 2)}{6 - (- 2)}$

Step 1.4.2

Rewrite the expression.

$m = 1$

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, $y = m x + b$ .

$y = (1) \cdot x + b$

Step 2.2

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

$y = (1) \cdot (- 2) + b$

Step 2.3

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

$- 2 = (1) \cdot (- 2) + b$

Step 2.4

Rewrite the equation as $(1) \cdot (- 2) + b = - 2$ .

$(1) \cdot (- 2) + b = - 2$

Step 2.5

Multiply $- 2$ by $1$ .

$- 2 + b = - 2$

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 $2$ to both sides of the equation.

$b = - 2 + 2$

Step 2.6.2

Add $- 2$ and $2$ .

$b = 0$

Step 3

List the slope and y-intercept.

Slope: $1$

y-intercept: $(0, 0)$

Step 4