Find the Slope and y-intercept (6,8) , (3,-9)

$(6, 8)$ , $(3, - 9)$

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.

$m = \frac{- 9 - (8)}{3 - (6)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $8$ .

$m = \frac{- 9 - 8}{3 - (6)}$

Subtract $8$ from $- 9$ .

$m = \frac{- 17}{3 - (6)}$

Simplify the denominator.

Multiply $- 1$ by $6$ .

$m = \frac{- 17}{3 - 6}$

Subtract $6$ from $3$ .

$m = \frac{- 17}{- 3}$

Dividing two negative values results in a positive value.

$m = \frac{17}{3}$

Step 2

Find the value of the y-intercept.

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

$y = (\frac{17}{3}) x + b$

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

$y = (\frac{17}{3}) \cdot (6) + b$

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

$8 = (\frac{17}{3}) \cdot (6) + b$

Rewrite the equation as $(\frac{17}{3}) \cdot (6) + b = 8$ .

$(\frac{17}{3}) \cdot (6) + b = 8$

Simplify each term.

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$\frac{17}{3} \cdot (3 (2)) + b = 8$

Cancel the common factor.

$\frac{17}{3} \cdot (3 \cdot 2) + b = 8$

Rewrite the expression.

$17 \cdot 2 + b = 8$

Multiply $17$ by $2$ .

$34 + b = 8$

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

Subtract $34$ from both sides of the equation.

$b = 8 - 34$

Subtract $34$ from $8$ .

$b = - 26$

Step 3

List the slope and y-intercept.

Slope: $\frac{17}{3}$

y-intercept: $(0, - 26)$

Step 4

Find the Slope and y-intercept (6,8) , (3,-9)

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