Find the Slope and y-intercept (-4,47) , (2,-16)

$(- 4, 47)$ , $(2, - 16)$

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.

$m = \frac{- 16 - (47)}{2 - (- 4)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $47$ .

$m = \frac{- 16 - 47}{2 - (- 4)}$

Subtract $47$ from $- 16$ .

$m = \frac{- 63}{2 - (- 4)}$

Simplify the denominator.

Multiply $- 1$ by $- 4$ .

$m = \frac{- 63}{2 + 4}$

Add $2$ and $4$ .

$m = \frac{- 63}{6}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $- 63$ and $6$ .

Factor $3$ out of $- 63$ .

$m = \frac{3 (- 21)}{6}$

Cancel the common factors.

Factor $3$ out of $6$ .

$m = \frac{3 \cdot - 21}{3 \cdot 2}$

Cancel the common factor.

$m = \frac{3 \cdot - 21}{3 \cdot 2}$

Rewrite the expression.

$m = \frac{- 21}{2}$

Move the negative in front of the fraction.

$m = - \frac{21}{2}$

Find the value of the y-intercept.

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

$y = (- \frac{21}{2}) \cdot x + b$

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

$y = (- \frac{21}{2}) \cdot (- 4) + b$

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

$47 = (- \frac{21}{2}) \cdot (- 4) + b$

Rewrite the equation as $(- \frac{21}{2}) \cdot (- 4) + b = 47$ .

$(- \frac{21}{2}) \cdot (- 4) + b = 47$

Simplify each term.

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{21}{2}$ into the numerator.

$\frac{- 21}{2} \cdot - 4 + b = 47$

Factor $2$ out of $- 4$ .

$\frac{- 21}{2} \cdot (2 (- 2)) + b = 47$

Cancel the common factor.

$\frac{- 21}{2} \cdot (2 \cdot - 2) + b = 47$

Rewrite the expression.

$- 21 \cdot - 2 + b = 47$

Multiply $- 21$ by $- 2$ .

$42 + b = 47$

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

Subtract $42$ from both sides of the equation.

$b = 47 - 42$

Subtract $42$ from $47$ .

$b = 5$

List the slope and y-intercept.

Slope: $- \frac{21}{2}$

y-intercept: $(0, 5)$

Find the Slope and y-intercept (-4,47) , (2,-16)

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