Find the Slope and y-intercept (-3,4) , (6,1)

$(- 3, 4)$ , $(6, 1)$

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.

$m = \frac{1 - (4)}{6 - (- 3)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $4$ .

$m = \frac{1 - 4}{6 - (- 3)}$

Subtract $4$ from $1$ .

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

Simplify the denominator.

Multiply $- 1$ by $- 3$ .

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

Add $6$ and $3$ .

$m = \frac{- 3}{9}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $- 3$ and $9$ .

Factor $3$ out of $- 3$ .

$m = \frac{3 (- 1)}{9}$

Cancel the common factors.

Factor $3$ out of $9$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Step 2

Find the value of the y-intercept.

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

$y = (- \frac{1}{3}) \cdot x + b$

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

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

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

$4 = (- \frac{1}{3}) \cdot (- 3) + b$

Rewrite the equation as $(- \frac{1}{3}) \cdot (- 3) + b = 4$ .

$(- \frac{1}{3}) \cdot (- 3) + b = 4$

Simplify each term.

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$\frac{- 1}{3} \cdot - 3 + b = 4$

Factor $3$ out of $- 3$ .

$\frac{- 1}{3} \cdot (3 (- 1)) + b = 4$

Cancel the common factor.

$\frac{- 1}{3} \cdot (3 \cdot - 1) + b = 4$

Rewrite the expression.

$- 1 \cdot - 1 + b = 4$

Multiply $- 1$ by $- 1$ .

$1 + b = 4$

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

Subtract $1$ from both sides of the equation.

$b = 4 - 1$

Subtract $1$ from $4$ .

$b = 3$

Step 3

List the slope and y-intercept.

Slope: $- \frac{1}{3}$

y-intercept: $(0, 3)$

Step 4

Find the Slope and y-intercept (-3,4) , (6,1)

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