Find the Slope and y-intercept (3,7) , (-2,-3)

$(3, 7)$ , $(- 2, - 3)$

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.

$m = \frac{- 3 - (7)}{- 2 - (3)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $7$ .

$m = \frac{- 3 - 7}{- 2 - (3)}$

Subtract $7$ from $- 3$ .

$m = \frac{- 10}{- 2 - (3)}$

Simplify the denominator.

Multiply $- 1$ by $3$ .

$m = \frac{- 10}{- 2 - 3}$

Subtract $3$ from $- 2$ .

$m = \frac{- 10}{- 5}$

Divide $- 10$ by $- 5$ .

$m = 2$

Step 2

Find the value of the y-intercept.

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

$y = (2) \cdot x + b$

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

$y = (2) \cdot (3) + b$

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

$7 = (2) \cdot (3) + b$

Rewrite the equation as $(2) \cdot (3) + b = 7$ .

$(2) \cdot (3) + b = 7$

Multiply $2$ by $3$ .

$6 + b = 7$

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

Subtract $6$ from both sides of the equation.

$b = 7 - 6$

Subtract $6$ from $7$ .

$b = 1$

Step 3

List the slope and y-intercept.

Slope: $2$

y-intercept: $(0, 1)$

Step 4

Find the Slope and y-intercept (3,7) , (-2,-3)

Related Questions

Support LCMGCF.com by disabling your adblocker.