Find the Slope and y-intercept (9,2) , (2,9)

$(9, 2)$ , $(2, 9)$

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.

$m = \frac{9 - (2)}{2 - (9)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $2$ .

$m = \frac{9 - 2}{2 - (9)}$

Subtract $2$ from $9$ .

$m = \frac{7}{2 - (9)}$

Simplify the denominator.

Multiply $- 1$ by $9$ .

$m = \frac{7}{2 - 9}$

Subtract $9$ from $2$ .

$m = \frac{7}{- 7}$

Divide $7$ by $- 7$ .

$m = - 1$

Step 2

Find the value of the y-intercept.

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

$y = (- 1) \cdot x + b$

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

$y = (- 1) \cdot (9) + b$

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

$2 = (- 1) \cdot (9) + b$

Rewrite the equation as $(- 1) \cdot (9) + b = 2$ .

$(- 1) \cdot (9) + b = 2$

Multiply $- 1$ by $9$ .

$- 9 + b = 2$

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

Add $9$ to both sides of the equation.

$b = 2 + 9$

Add $2$ and $9$ .

$b = 11$

Step 3

List the slope and y-intercept.

Slope: $- 1$

y-intercept: $(0, 11)$

Step 4

Find the Slope and y-intercept (9,2) , (2,9)

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