Find the Slope and y-intercept (6,12) , (7,14)

$(6, 12)$ , $(7, 14)$

Find the value of the slope.

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

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

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).

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

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

$m = \frac{14 - (12)}{7 - (6)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $12$ .

$m = \frac{14 - 12}{7 - (6)}$

Subtract $12$ from $14$ .

$m = \frac{2}{7 - (6)}$

Simplify the denominator.

Multiply $- 1$ by $6$ .

$m = \frac{2}{7 - 6}$

Subtract $6$ from $7$ .

$m = \frac{2}{1}$

Divide $2$ by $1$ .

$m = 2$

Find the value of the y-intercept.

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

$y = (2) \cdot x + b$

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

$y = (2) \cdot (6) + b$

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

$12 = (2) \cdot (6) + b$

Rewrite the equation as $(2) \cdot (6) + b = 12$ .

$(2) \cdot (6) + b = 12$

Multiply $2$ by $6$ .

$12 + b = 12$

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

Subtract $12$ from both sides of the equation.

$b = 12 - 12$

Subtract $12$ from $12$ .

$b = 0$

List the slope and y-intercept.

Slope: $2$

y-intercept: $(0, 0)$

Find the Slope and y-intercept (6,12) , (7,14)

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