Find the Equation Using Point-Slope Formula (8,16) , (9,18)

$(8, 16)$ , $(9, 18)$

Step 1

Find the slope of the line between $(8, 16)$ and $(9, 18)$ 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.

$m = \frac{18 - (16)}{9 - (8)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $16$ .

$m = \frac{18 - 16}{9 - (8)}$

Subtract $16$ from $18$ .

$m = \frac{2}{9 - (8)}$

Simplify the denominator.

Multiply $- 1$ by $8$ .

$m = \frac{2}{9 - 8}$

Subtract $8$ from $9$ .

$m = \frac{2}{1}$

Divide $2$ by $1$ .

$m = 2$

Step 2

Use the slope $2$ and a given point $(8, 16)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (16) = 2 \cdot (x - (8))$

Step 3

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

$y - 16 = 2 \cdot (x - 8)$

Step 4

Solve for $y$ .

Simplify $2 \cdot (x - 8)$ .

Rewrite.

$y - 16 = 0 + 0 + 2 \cdot (x - 8)$

Simplify by adding zeros.

$y - 16 = 2 \cdot (x - 8)$

Apply the distributive property.

$y - 16 = 2 x + 2 \cdot - 8$

Multiply $2$ by $- 8$ .

$y - 16 = 2 x - 16$

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

Add $16$ to both sides of the equation.

$y = 2 x - 16 + 16$

Combine the opposite terms in $2 x - 16 + 16$ .

Add $- 16$ and $16$ .

$y = 2 x + 0$

Add $2 x$ and $0$ .

$y = 2 x$

Step 5

List the equation in different forms.

Slope-intercept form:

$y = 2 x$

Point-slope form:

$y - 16 = 2 \cdot (x - 8)$

Step 6

Find the Equation Using Point-Slope Formula (8,16) , (9,18)

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