Write in Standard Form (-1,19) and (3,35)

$(- 1, 19)$ and $(3, 35)$

Find the slope of the line between $(- 1, 19)$ and $(3, 35)$ 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.

$m = \frac{35 - (19)}{3 - (- 1)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $19$ .

$m = \frac{35 - 19}{3 - (- 1)}$

Subtract $19$ from $35$ .

$m = \frac{16}{3 - (- 1)}$

Simplify the denominator.

Multiply $- 1$ by $- 1$ .

$m = \frac{16}{3 + 1}$

Add $3$ and $1$ .

$m = \frac{16}{4}$

Divide $16$ by $4$ .

$m = 4$

Use the slope $4$ and a given point $(- 1, 19)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (19) = 4 \cdot (x - (- 1))$

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

$y - 19 = 4 \cdot (x + 1)$

Write the equation in standard form.

The standard form of a linear equation is $A x + B y = C$ .

Simplify the right side.

Simplify $4 \cdot (x + 1)$ .

Apply the distributive property.

$y - 19 = 4 x + 4 \cdot 1$

Multiply $4$ by $1$ .

$y - 19 = 4 x + 4$

Rewrite the equation.

$4 x + 4 = y - 19$

Move all terms containing variables to the left side of the equation.

Subtract $y$ from both sides of the equation.

$4 x + 4 - y = - 19$

Move $4$ .

$4 x - y + 4 = - 19$

Move all terms not containing a variable to the right side of the equation.

Subtract $4$ from both sides of the equation.

$4 x - y = - 19 - 4$

Subtract $4$ from $- 19$ .

$4 x - y = - 23$

Write in Standard Form (-1,19) and (3,35)

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