Find the Slope and y-intercept (8,-16) , (1,5)

$(8, - 16)$ , $(1, 5)$

Step 1

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.

$m = \frac{5 - (- 16)}{1 - (8)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 16$ .

$m = \frac{5 + 16}{1 - (8)}$

Add $5$ and $16$ .

$m = \frac{21}{1 - (8)}$

Simplify the denominator.

Multiply $- 1$ by $8$ .

$m = \frac{21}{1 - 8}$

Subtract $8$ from $1$ .

$m = \frac{21}{- 7}$

Divide $21$ by $- 7$ .

$m = - 3$

Step 2

Find the value of the y-intercept.

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

$y = (- 3) \cdot x + b$

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

$y = (- 3) \cdot (8) + b$

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

$- 16 = (- 3) \cdot (8) + b$

Rewrite the equation as $(- 3) \cdot (8) + b = - 16$ .

$(- 3) \cdot (8) + b = - 16$

Multiply $- 3$ by $8$ .

$- 24 + b = - 16$

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

Add $24$ to both sides of the equation.

$b = - 16 + 24$

Add $- 16$ and $24$ .

$b = 8$

Step 3

List the slope and y-intercept.

Slope: $- 3$

y-intercept: $(0, 8)$

Step 4

Find the Slope and y-intercept (8,-16) , (1,5)

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