Find the Slope and y-intercept (-4,0) , (0,5)

$(- 4, 0)$ , $(0, 5)$

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.

$m = \frac{5 - (0)}{0 - (- 4)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $0$ .

$m = \frac{5 + 0}{0 - (- 4)}$

Add $5$ and $0$ .

$m = \frac{5}{0 - (- 4)}$

Simplify the denominator.

Multiply $- 1$ by $- 4$ .

$m = \frac{5}{0 + 4}$

Add $0$ and $4$ .

$m = \frac{5}{4}$

Step 2

Find the value of the y-intercept.

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

$y = (\frac{5}{4}) x + b$

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

$y = (\frac{5}{4}) \cdot (- 4) + b$

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

$0 = (\frac{5}{4}) \cdot (- 4) + b$

Rewrite the equation as $(\frac{5}{4}) \cdot (- 4) + b = 0$ .

$(\frac{5}{4}) \cdot (- 4) + b = 0$

Simplify each term.

Cancel the common factor of $4$ .

Factor $4$ out of $- 4$ .

$\frac{5}{4} \cdot (4 (- 1)) + b = 0$

Cancel the common factor.

$\frac{5}{4} \cdot (4 \cdot - 1) + b = 0$

Rewrite the expression.

$5 \cdot - 1 + b = 0$

Multiply $5$ by $- 1$ .

$- 5 + b = 0$

Add $5$ to both sides of the equation.

$b = 5$

Step 3

List the slope and y-intercept.

Slope: $\frac{5}{4}$

y-intercept: $(0, 5)$

Step 4

Find the Slope and y-intercept (-4,0) , (0,5)

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