Find the Equation Using Point-Slope Formula (1,0) , (7,7)

$(1, 0)$ , $(7, 7)$

Step 1

Find the slope of the line between $(1, 0)$ and $(7, 7)$ 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.

$m = \frac{7 - (0)}{7 - (1)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $0$ .

$m = \frac{7 + 0}{7 - (1)}$

Add $7$ and $0$ .

$m = \frac{7}{7 - (1)}$

Simplify the denominator.

Multiply $- 1$ by $1$ .

$m = \frac{7}{7 - 1}$

Subtract $1$ from $7$ .

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

Step 2

Use the slope $\frac{7}{6}$ and a given point $(1, 0)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (0) = \frac{7}{6} \cdot (x - (1))$

Step 3

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

$y + 0 = \frac{7}{6} \cdot (x - 1)$

Step 4

Solve for $y$ .

Add $y$ and $0$ .

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

Simplify $\frac{7}{6} \cdot (x - 1)$ .

Apply the distributive property.

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

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

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

Multiply $\frac{7}{6} \cdot - 1$ .

Combine $\frac{7}{6}$ and $- 1$ .

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

Multiply $7$ by $- 1$ .

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

Move the negative in front of the fraction.

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

Step 5

Reorder terms.

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

Step 6

List the equation in different forms.

Slope-intercept form:

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

Point-slope form:

$y + 0 = \frac{7}{6} \cdot (x - 1)$

Step 7

Find the Equation Using Point-Slope Formula (1,0) , (7,7)

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