Find the Equation Using Point-Slope Formula (46,338) , (64,392)

$(46, 338)$ , $(64, 392)$

Step 1

Find the slope of the line between $(46, 338)$ and $(64, 392)$ 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.

$m = \frac{392 - (338)}{64 - (46)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $338$ .

$m = \frac{392 - 338}{64 - (46)}$

Subtract $338$ from $392$ .

$m = \frac{54}{64 - (46)}$

Simplify the denominator.

Multiply $- 1$ by $46$ .

$m = \frac{54}{64 - 46}$

Subtract $46$ from $64$ .

$m = \frac{54}{18}$

Divide $54$ by $18$ .

$m = 3$

Step 2

Use the slope $3$ and a given point $(46, 338)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (338) = 3 \cdot (x - (46))$

Step 3

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

$y - 338 = 3 \cdot (x - 46)$

Step 4

Solve for $y$ .

Simplify $3 \cdot (x - 46)$ .

Rewrite.

$y - 338 = 0 + 0 + 3 \cdot (x - 46)$

Simplify by adding zeros.

$y - 338 = 3 \cdot (x - 46)$

Apply the distributive property.

$y - 338 = 3 x + 3 \cdot - 46$

Multiply $3$ by $- 46$ .

$y - 338 = 3 x - 138$

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

Add $338$ to both sides of the equation.

$y = 3 x - 138 + 338$

Add $- 138$ and $338$ .

$y = 3 x + 200$

Step 5

List the equation in different forms.

Slope-intercept form:

$y = 3 x + 200$

Point-slope form:

$y - 338 = 3 \cdot (x - 46)$

Step 6

Find the Equation Using Point-Slope Formula (46,338) , (64,392)

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