Find the Slope and y-intercept (-2,1) , (4,-2)

$(- 2, 1)$ , $(4, - 2)$

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.

$m = \frac{- 2 - (1)}{4 - (- 2)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $1$ .

$m = \frac{- 2 - 1}{4 - (- 2)}$

Subtract $1$ from $- 2$ .

$m = \frac{- 3}{4 - (- 2)}$

Simplify the denominator.

Multiply $- 1$ by $- 2$ .

$m = \frac{- 3}{4 + 2}$

Add $4$ and $2$ .

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

Reduce the expression by cancelling the common factors.

Cancel the common factor of $- 3$ and $6$ .

Factor $3$ out of $- 3$ .

$m = \frac{3 (- 1)}{6}$

Cancel the common factors.

Factor $3$ out of $6$ .

$m = \frac{3 \cdot - 1}{3 \cdot 2}$

Cancel the common factor.

$m = \frac{3 \cdot - 1}{3 \cdot 2}$

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Step 2

Find the value of the y-intercept.

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

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

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

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

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

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

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

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

Simplify each term.

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$\frac{- 1}{2} \cdot - 2 + b = 1$

Factor $2$ out of $- 2$ .

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

Cancel the common factor.

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

Rewrite the expression.

$- 1 \cdot - 1 + b = 1$

Multiply $- 1$ by $- 1$ .

$1 + b = 1$

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

Subtract $1$ from both sides of the equation.

$b = 1 - 1$

Subtract $1$ from $1$ .

$b = 0$

Step 3

List the slope and y-intercept.

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

y-intercept: $(0, 0)$

Step 4

Find the Slope and y-intercept (-2,1) , (4,-2)

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