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

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

Step 1

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

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

Simplify.

Simplify the numerator.

Multiply $- 1$ by $3$ .

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

Subtract $3$ from $- 4$ .

$m = \frac{- 7}{- 4 - (4)}$

Simplify the denominator.

Multiply $- 1$ by $4$ .

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

Subtract $4$ from $- 4$ .

$m = \frac{- 7}{- 8}$

Dividing two negative values results in a positive value.

$m = \frac{7}{8}$

Step 2

Use the slope $\frac{7}{8}$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (3) = \frac{7}{8} \cdot (x - (4))$

Step 3

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

$y - 3 = \frac{7}{8} \cdot (x - 4)$

Step 4

Solve for $y$ .

Simplify $\frac{7}{8} \cdot (x - 4)$ .

Rewrite.

$y - 3 = 0 + 0 + \frac{7}{8} \cdot (x - 4)$

Simplify by adding zeros.

$y - 3 = \frac{7}{8} \cdot (x - 4)$

Apply the distributive property.

$y - 3 = \frac{7}{8} x + \frac{7}{8} \cdot - 4$

Combine $\frac{7}{8}$ and $x$ .

$y - 3 = \frac{7 x}{8} + \frac{7}{8} \cdot - 4$

Cancel the common factor of $4$ .

Factor $4$ out of $8$ .

$y - 3 = \frac{7 x}{8} + \frac{7}{4 (2)} \cdot - 4$

Factor $4$ out of $- 4$ .

$y - 3 = \frac{7 x}{8} + \frac{7}{4 \cdot 2} \cdot (4 \cdot - 1)$

Cancel the common factor.

$y - 3 = \frac{7 x}{8} + \frac{7}{4 \cdot 2} \cdot (4 \cdot - 1)$

Rewrite the expression.

$y - 3 = \frac{7 x}{8} + \frac{7}{2} \cdot - 1$

Combine $\frac{7}{2}$ and $- 1$ .

$y - 3 = \frac{7 x}{8} + \frac{7 \cdot - 1}{2}$

Simplify the expression.

Multiply $7$ by $- 1$ .

$y - 3 = \frac{7 x}{8} + \frac{- 7}{2}$

Move the negative in front of the fraction.

$y - 3 = \frac{7 x}{8} - \frac{7}{2}$

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

Add $3$ to both sides of the equation.

$y = \frac{7 x}{8} - \frac{7}{2} + 3$

To write $3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = \frac{7 x}{8} - \frac{7}{2} + 3 \cdot \frac{2}{2}$

Combine $3$ and $\frac{2}{2}$ .

$y = \frac{7 x}{8} - \frac{7}{2} + \frac{3 \cdot 2}{2}$

Combine the numerators over the common denominator.

$y = \frac{7 x}{8} + \frac{- 7 + 3 \cdot 2}{2}$

Simplify the numerator.

Multiply $3$ by $2$ .

$y = \frac{7 x}{8} + \frac{- 7 + 6}{2}$

Add $- 7$ and $6$ .

$y = \frac{7 x}{8} + \frac{- 1}{2}$

Move the negative in front of the fraction.

$y = \frac{7 x}{8} - \frac{1}{2}$

Step 5

Reorder terms.

$y = \frac{7}{8} x - \frac{1}{2}$

Step 6

List the equation in different forms.

Slope-intercept form:

$y = \frac{7}{8} x - \frac{1}{2}$

Point-slope form:

$y - 3 = \frac{7}{8} \cdot (x - 4)$

Step 7

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

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