Find the Slope and y-intercept (-5,3) , (7,9)

$(- 5, 3)$ , $(7, 9)$

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.

$m = \frac{9 - (3)}{7 - (- 5)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $3$ .

$m = \frac{9 - 3}{7 - (- 5)}$

Subtract $3$ from $9$ .

$m = \frac{6}{7 - (- 5)}$

Simplify the denominator.

Multiply $- 1$ by $- 5$ .

$m = \frac{6}{7 + 5}$

Add $7$ and $5$ .

$m = \frac{6}{12}$

Cancel the common factor of $6$ and $12$ .

Factor $6$ out of $6$ .

$m = \frac{6 (1)}{12}$

Cancel the common factors.

Factor $6$ out of $12$ .

$m = \frac{6 \cdot 1}{6 \cdot 2}$

Cancel the common factor.

$m = \frac{6 \cdot 1}{6 \cdot 2}$

Rewrite the expression.

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

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, $y = m x + b$ .

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

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

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

Rewrite the equation as $(\frac{1}{2}) \cdot (- 5) + b = 3$ .

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

Simplify each term.

Combine $\frac{1}{2}$ and $- 5$ .

$\frac{- 5}{2} + b = 3$

Move the negative in front of the fraction.

$- \frac{5}{2} + b = 3$

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

Add $\frac{5}{2}$ to both sides of the equation.

$b = 3 + \frac{5}{2}$

To write $3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$b = 3 \cdot \frac{2}{2} + \frac{5}{2}$

Combine $3$ and $\frac{2}{2}$ .

$b = \frac{3 \cdot 2}{2} + \frac{5}{2}$

Combine the numerators over the common denominator.

$b = \frac{3 \cdot 2 + 5}{2}$

Simplify the numerator.

Multiply $3$ by $2$ .

$b = \frac{6 + 5}{2}$

Add $6$ and $5$ .

$b = \frac{11}{2}$

List the slope and y-intercept.

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

y-intercept: $(0, \frac{11}{2})$

Find the Slope and y-intercept (-5,3) , (7,9)

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