Find the Slope and y-intercept (4,-3) , (8,5)

$(4, - 3)$ , $(8, 5)$

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.

$m = \frac{5 - (- 3)}{8 - (4)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 3$ .

$m = \frac{5 + 3}{8 - (4)}$

Add $5$ and $3$ .

$m = \frac{8}{8 - (4)}$

Simplify the denominator.

Multiply $- 1$ by $4$ .

$m = \frac{8}{8 - 4}$

Subtract $4$ from $8$ .

$m = \frac{8}{4}$

Divide $8$ by $4$ .

$m = 2$

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, $y = m x + b$ .

$y = (2) \cdot (4) + b$

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

$- 3 = (2) \cdot (4) + b$

Rewrite the equation as $(2) \cdot (4) + b = - 3$ .

$(2) \cdot (4) + b = - 3$

Multiply $2$ by $4$ .

$8 + b = - 3$

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

Subtract $8$ from both sides of the equation.

$b = - 3 - 8$

Subtract $8$ from $- 3$ .

$b = - 11$

List the slope and y-intercept.

Slope: $2$

y-intercept: $(0, - 11)$

Find the Slope and y-intercept (4,-3) , (8,5)

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