Find the Slope and y-intercept (-1,0) , (0,3)

$(- 1, 0)$ , $(0, 3)$

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.

$m = \frac{3 - (0)}{0 - (- 1)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $0$ .

$m = \frac{3 + 0}{0 - (- 1)}$

Add $3$ and $0$ .

$m = \frac{3}{0 - (- 1)}$

Simplify the denominator.

Multiply $- 1$ by $- 1$ .

$m = \frac{3}{0 + 1}$

Add $0$ and $1$ .

$m = \frac{3}{1}$

Divide $3$ by $1$ .

$m = 3$

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, $y = m x + b$ .

$y = (3) \cdot (- 1) + b$

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

$0 = (3) \cdot (- 1) + b$

Rewrite the equation as $(3) \cdot (- 1) + b = 0$ .

$(3) \cdot (- 1) + b = 0$

Multiply $3$ by $- 1$ .

$- 3 + b = 0$

Add $3$ to both sides of the equation.

$b = 3$

Step 3

List the slope and y-intercept.

Slope: $3$

y-intercept: $(0, 3)$

Step 4

Find the Slope and y-intercept (-1,0) , (0,3)

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