Find the Equation Using Point-Slope Formula (-4,-3) , (4,11)

$(- 4, - 3)$ , $(4, 11)$

Step 1

Find the slope of the line between $(- 4, - 3)$ and $(4, 11)$ 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.

$m = \frac{11 - (- 3)}{4 - (- 4)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 3$ .

$m = \frac{11 + 3}{4 - (- 4)}$

Add $11$ and $3$ .

$m = \frac{14}{4 - (- 4)}$

Simplify the denominator.

Multiply $- 1$ by $- 4$ .

$m = \frac{14}{4 + 4}$

Add $4$ and $4$ .

$m = \frac{14}{8}$

Cancel the common factor of $14$ and $8$ .

Factor $2$ out of $14$ .

$m = \frac{2 (7)}{8}$

Cancel the common factors.

Factor $2$ out of $8$ .

$m = \frac{2 \cdot 7}{2 \cdot 4}$

Cancel the common factor.

$m = \frac{2 \cdot 7}{2 \cdot 4}$

Rewrite the expression.

$m = \frac{7}{4}$

Step 2

Use the slope $\frac{7}{4}$ and a given point $(- 4, - 3)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 3) = \frac{7}{4} \cdot (x - (- 4))$

Step 3

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

$y + 3 = \frac{7}{4} \cdot (x + 4)$

Step 4

Solve for $y$ .

Simplify $\frac{7}{4} \cdot (x + 4)$ .

Rewrite.

$y + 3 = 0 + 0 + \frac{7}{4} \cdot (x + 4)$

Simplify by adding zeros.

$y + 3 = \frac{7}{4} \cdot (x + 4)$

Apply the distributive property.

$y + 3 = \frac{7}{4} x + \frac{7}{4} \cdot 4$

Combine $\frac{7}{4}$ and $x$ .

$y + 3 = \frac{7 x}{4} + \frac{7}{4} \cdot 4$

Cancel the common factor of $4$ .

Cancel the common factor.

$y + 3 = \frac{7 x}{4} + \frac{7}{4} \cdot 4$

Rewrite the expression.

$y + 3 = \frac{7 x}{4} + 7$

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

Subtract $3$ from both sides of the equation.

$y = \frac{7 x}{4} + 7 - 3$

Subtract $3$ from $7$ .

$y = \frac{7 x}{4} + 4$

Step 5

Reorder terms.

$y = \frac{7}{4} x + 4$

Step 6

List the equation in different forms.

Slope-intercept form:

$y = \frac{7}{4} x + 4$

Point-slope form:

$y + 3 = \frac{7}{4} \cdot (x + 4)$

Step 7

Find the Equation Using Point-Slope Formula (-4,-3) , (4,11)

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