Find the Equation Using Point-Slope Formula (6,7) , (0,0)

$(6, 7)$ , $(0, 0)$

Step 1

Find the slope of the line between $(6, 7)$ and $(0, 0)$ 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.

$m = \frac{0 - (7)}{0 - (6)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $7$ .

$m = \frac{0 - 7}{0 - (6)}$

Subtract $7$ from $0$ .

$m = \frac{- 7}{0 - (6)}$

Simplify the denominator.

Multiply $- 1$ by $6$ .

$m = \frac{- 7}{0 - 6}$

Subtract $6$ from $0$ .

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

Dividing two negative values results in a positive value.

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

Step 2

Use the slope $\frac{7}{6}$ and a given point $(6, 7)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (7) = \frac{7}{6} \cdot (x - (6))$

Step 3

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

$y - 7 = \frac{7}{6} \cdot (x - 6)$

Step 4

Solve for $y$ .

Simplify $\frac{7}{6} \cdot (x - 6)$ .

Rewrite.

$y - 7 = 0 + 0 + \frac{7}{6} \cdot (x - 6)$

Simplify by adding zeros.

$y - 7 = \frac{7}{6} \cdot (x - 6)$

Apply the distributive property.

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

Combine $\frac{7}{6}$ and $x$ .

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

Cancel the common factor of $6$ .

Factor $6$ out of $- 6$ .

$y - 7 = \frac{7 x}{6} + \frac{7}{6} \cdot (6 (- 1))$

Cancel the common factor.

$y - 7 = \frac{7 x}{6} + \frac{7}{6} \cdot (6 \cdot - 1)$

Rewrite the expression.

$y - 7 = \frac{7 x}{6} + 7 \cdot - 1$

Multiply $7$ by $- 1$ .

$y - 7 = \frac{7 x}{6} - 7$

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

Add $7$ to both sides of the equation.

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

Combine the opposite terms in $\frac{7 x}{6} - 7 + 7$ .

Add $- 7$ and $7$ .

$y = \frac{7 x}{6} + 0$

Add $\frac{7 x}{6}$ and $0$ .

$y = \frac{7 x}{6}$

Step 5

Reorder terms.

$y = \frac{7}{6} x$

Step 6

List the equation in different forms.

Slope-intercept form:

$y = \frac{7}{6} x$

Point-slope form:

$y - 7 = \frac{7}{6} \cdot (x - 6)$

Step 7

Find the Equation Using Point-Slope Formula (6,7) , (0,0)

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