Write in Slope-Intercept Form (2,-1) and (4,5)

$(2, - 1)$ and $(4, 5)$

Find the slope of the line between $(2, - 1)$ and $(4, 5)$ 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.

$m = \frac{5 - (- 1)}{4 - (2)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 1$ .

$m = \frac{5 + 1}{4 - (2)}$

Add $5$ and $1$ .

$m = \frac{6}{4 - (2)}$

Simplify the denominator.

Multiply $- 1$ by $2$ .

$m = \frac{6}{4 - 2}$

Subtract $2$ from $4$ .

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

Divide $6$ by $2$ .

$m = 3$

Use the slope $3$ and a given point $(2, - 1)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 1) = 3 \cdot (x - (2))$

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

$y + 1 = 3 \cdot (x - 2)$

Solve for $y$ .

Simplify $3 \cdot (x - 2)$ .

Rewrite.

$y + 1 = 0 + 0 + 3 \cdot (x - 2)$

Simplify by adding zeros.

$y + 1 = 3 \cdot (x - 2)$

Apply the distributive property.

$y + 1 = 3 x + 3 \cdot - 2$

Multiply $3$ by $- 2$ .

$y + 1 = 3 x - 6$

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

Subtract $1$ from both sides of the equation.

$y = 3 x - 6 - 1$

Subtract $1$ from $- 6$ .

$y = 3 x - 7$

Write in Slope-Intercept Form (2,-1) and (4,5)

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