Write in Slope-Intercept Form (1,-2) , (3,3)

$(1, - 2)$ , $(3, 3)$

Step 1

Find the slope of the line between $(1, - 2)$ and $(3, 3)$ using $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ , which is the change of $y$ over the change of $x$ .

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.

$m = \frac{3 - (- 2)}{3 - (1)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 2$ .

$m = \frac{3 + 2}{3 - (1)}$

Add $3$ and $2$ .

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

Simplify the denominator.

Multiply $- 1$ by $1$ .

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

Subtract $1$ from $3$ .

$m = \frac{5}{2}$

Step 2

Use the slope $\frac{5}{2}$ and a given point $(1, - 2)$ to substitute for $x_{1}$ and $y_{1}$ in the point-slope form $y - y_{1} = m (x - x_{1})$ , which is derived from the slope equation $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 2) = \frac{5}{2} \cdot (x - (1))$

Step 3

Simplify the equation and keep it in point-slope form.

$y + 2 = \frac{5}{2} \cdot (x - 1)$

Step 4

Write the equation in $y = m x + b$ form.

Solve for $y$ .

Simplify $\frac{5}{2} \cdot (x - 1)$ .

Rewrite.

$y + 2 = 0 + 0 + \frac{5}{2} \cdot (x - 1)$

Simplify by adding zeros.

$y + 2 = \frac{5}{2} \cdot (x - 1)$

Apply the distributive property.

$y + 2 = \frac{5}{2} x + \frac{5}{2} \cdot - 1$

Combine $\frac{5}{2}$ and $x$ .

$y + 2 = \frac{5 x}{2} + \frac{5}{2} \cdot - 1$

Multiply $\frac{5}{2} \cdot - 1$ .

Combine $\frac{5}{2}$ and $- 1$ .

$y + 2 = \frac{5 x}{2} + \frac{5 \cdot - 1}{2}$

Multiply $5$ by $- 1$ .

$y + 2 = \frac{5 x}{2} + \frac{- 5}{2}$

Move the negative in front of the fraction.

$y + 2 = \frac{5 x}{2} - \frac{5}{2}$

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

Subtract $2$ from both sides of the equation.

$y = \frac{5 x}{2} - \frac{5}{2} - 2$

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = \frac{5 x}{2} - \frac{5}{2} - 2 \cdot \frac{2}{2}$

Combine $- 2$ and $\frac{2}{2}$ .

$y = \frac{5 x}{2} - \frac{5}{2} + \frac{- 2 \cdot 2}{2}$

Combine the numerators over the common denominator.

$y = \frac{5 x}{2} + \frac{- 5 - 2 \cdot 2}{2}$

Simplify the numerator.

Multiply $- 2$ by $2$ .

$y = \frac{5 x}{2} + \frac{- 5 - 4}{2}$

Subtract $4$ from $- 5$ .

$y = \frac{5 x}{2} + \frac{- 9}{2}$

Move the negative in front of the fraction.

$y = \frac{5 x}{2} - \frac{9}{2}$

Reorder terms.

$y = \frac{5}{2} x - \frac{9}{2}$

Step 5

Write in Slope-Intercept Form (1,-2) , (3,3)

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