Find the Slope and y-intercept (8,0) , (3,7)

$(8, 0)$ , $(3, 7)$

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.

$m = \frac{7 - (0)}{3 - (8)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $0$ .

$m = \frac{7 + 0}{3 - (8)}$

Add $7$ and $0$ .

$m = \frac{7}{3 - (8)}$

Simplify the denominator.

Multiply $- 1$ by $8$ .

$m = \frac{7}{3 - 8}$

Subtract $8$ from $3$ .

$m = \frac{7}{- 5}$

Move the negative in front of the fraction.

$m = - \frac{7}{5}$

Step 2

Find the value of the y-intercept.

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

$y = (- \frac{7}{5}) \cdot x + b$

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

$y = (- \frac{7}{5}) \cdot (8) + b$

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

$0 = (- \frac{7}{5}) \cdot (8) + b$

Rewrite the equation as $(- \frac{7}{5}) \cdot (8) + b = 0$ .

$(- \frac{7}{5}) \cdot (8) + b = 0$

Simplify each term.

Multiply $(- \frac{7}{5}) (8)$ .

Multiply $8$ by $- 1$ .

$- 8 (\frac{7}{5}) + b = 0$

Combine $- 8$ and $\frac{7}{5}$ .

$\frac{- 8 \cdot 7}{5} + b = 0$

Multiply $- 8$ by $7$ .

$\frac{- 56}{5} + b = 0$

Move the negative in front of the fraction.

$- \frac{56}{5} + b = 0$

Add $\frac{56}{5}$ to both sides of the equation.

$b = \frac{56}{5}$

Step 3

List the slope and y-intercept.

Slope: $- \frac{7}{5}$

y-intercept: $(0, \frac{56}{5})$

Step 4

Find the Slope and y-intercept (8,0) , (3,7)

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