Find the Slope and y-intercept (-6,-5) , (-4,-4)

$(- 6, - 5)$ , $(- 4, - 4)$

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.

$m = \frac{- 4 - (- 5)}{- 4 - (- 6)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 5$ .

$m = \frac{- 4 + 5}{- 4 - (- 6)}$

Add $- 4$ and $5$ .

$m = \frac{1}{- 4 - (- 6)}$

Simplify the denominator.

Multiply $- 1$ by $- 6$ .

$m = \frac{1}{- 4 + 6}$

Add $- 4$ and $6$ .

$m = \frac{1}{2}$

Step 2

Find the value of the y-intercept.

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

$y = (\frac{1}{2}) x + b$

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

$y = (\frac{1}{2}) \cdot (- 6) + b$

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

$- 5 = (\frac{1}{2}) \cdot (- 6) + b$

Rewrite the equation as $(\frac{1}{2}) \cdot (- 6) + b = - 5$ .

$(\frac{1}{2}) \cdot (- 6) + b = - 5$

Cancel the common factor of $2$ .

Factor $2$ out of $- 6$ .

$\frac{1}{2} \cdot (2 (- 3)) + b = - 5$

Cancel the common factor.

$\frac{1}{2} \cdot (2 \cdot - 3) + b = - 5$

Rewrite the expression.

$- 3 + b = - 5$

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

Add $3$ to both sides of the equation.

$b = - 5 + 3$

Add $- 5$ and $3$ .

$b = - 2$

Step 3

List the slope and y-intercept.

Slope: $\frac{1}{2}$

y-intercept: $(0, - 2)$

Step 4

Find the Slope and y-intercept (-6,-5) , (-4,-4)

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