Find the Slope and y-intercept (1,-1) , (3,5)

$(1, - 1)$ , $(3, 5)$

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.

$m = \frac{5 - (- 1)}{3 - (1)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 1$ .

$m = \frac{5 + 1}{3 - (1)}$

Add $5$ and $1$ .

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

Simplify the denominator.

Multiply $- 1$ by $1$ .

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

Subtract $1$ from $3$ .

$m = \frac{6}{2}$

Divide $6$ by $2$ .

$m = 3$

Step 2

Find the value of the y-intercept.

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

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

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

$y = (3) \cdot (1) + b$

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

$- 1 = (3) \cdot (1) + b$

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

$(3) \cdot (1) + b = - 1$

Multiply $3$ by $1$ .

$3 + b = - 1$

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

Subtract $3$ from both sides of the equation.

$b = - 1 - 3$

Subtract $3$ from $- 1$ .

$b = - 4$

Step 3

List the slope and y-intercept.

Slope: $3$

y-intercept: $(0, - 4)$

Step 4

Find the Slope and y-intercept (1,-1) , (3,5)

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