Find the Equation Using Point-Slope Formula (7,11) , (13,17)

$(7, 11)$ , $(13, 17)$

Step 1

Find the slope of the line between $(7, 11)$ and $(13, 17)$ 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.

$m = \frac{17 - (11)}{13 - (7)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $11$ .

$m = \frac{17 - 11}{13 - (7)}$

Subtract $11$ from $17$ .

$m = \frac{6}{13 - (7)}$

Simplify the denominator.

Multiply $- 1$ by $7$ .

$m = \frac{6}{13 - 7}$

Subtract $7$ from $13$ .

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

Divide $6$ by $6$ .

$m = 1$

Step 2

Use the slope $1$ and a given point $(7, 11)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (11) = 1 \cdot (x - (7))$

Step 3

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

$y - 11 = 1 \cdot (x - 7)$

Step 4

Solve for $y$ .

Multiply $x - 7$ by $1$ .

$y - 11 = x - 7$

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

Add $11$ to both sides of the equation.

$y = x - 7 + 11$

Add $- 7$ and $11$ .

$y = x + 4$

Step 5

List the equation in different forms.

Slope-intercept form:

$y = x + 4$

Point-slope form:

$y - 11 = 1 \cdot (x - 7)$

Step 6

Find the Equation Using Point-Slope Formula (7,11) , (13,17)

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