Find the Slope and y-intercept (-3,-5) , (0,10)

$(- 3, - 5)$ , $(0, 10)$

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.

$m = \frac{10 - (- 5)}{0 - (- 3)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 5$ .

$m = \frac{10 + 5}{0 - (- 3)}$

Add $10$ and $5$ .

$m = \frac{15}{0 - (- 3)}$

Simplify the denominator.

Multiply $- 1$ by $- 3$ .

$m = \frac{15}{0 + 3}$

Add $0$ and $3$ .

$m = \frac{15}{3}$

Divide $15$ by $3$ .

$m = 5$

Step 2

Find the value of the y-intercept.

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

$y = (5) \cdot x + b$

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

$y = (5) \cdot (- 3) + b$

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

$- 5 = (5) \cdot (- 3) + b$

Rewrite the equation as $(5) \cdot (- 3) + b = - 5$ .

$(5) \cdot (- 3) + b = - 5$

Multiply $5$ by $- 3$ .

$- 15 + b = - 5$

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

Add $15$ to both sides of the equation.

$b = - 5 + 15$

Add $- 5$ and $15$ .

$b = 10$

Step 3

List the slope and y-intercept.

Slope: $5$

y-intercept: $(0, 10)$

Step 4

Find the Slope and y-intercept (-3,-5) , (0,10)

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