Find the Equation Using Two Points (7,0) , (-5,4)

$(7, 0)$ , $(- 5, 4)$

Step 1

Use $y = m x + b$ to calculate the equation of the line, where $m$ represents the slope and $b$ represents the y-intercept.

To calculate the equation of the line, use the $y = m x + b$ format.

Step 2

Slope is equal to the change in $y$ over the change in $x$ , or rise over run.

$m = \frac{(change in y)}{(change in x)}$

Step 3

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).

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

Step 4

Substitute in the values of $x$ and $y$ into the equation to find the slope.

$m = \frac{4 - (0)}{- 5 - (7)}$

Step 5

Finding the slope $m$ .

Simplify the numerator.

Multiply $- 1$ by $0$ .

$m = \frac{4 + 0}{- 5 - (7)}$

Add $4$ and $0$ .

$m = \frac{4}{- 5 - (7)}$

Simplify the denominator.

Multiply $- 1$ by $7$ .

$m = \frac{4}{- 5 - 7}$

Subtract $7$ from $- 5$ .

$m = \frac{4}{- 12}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $4$ and $- 12$ .

Factor $4$ out of $4$ .

$m = \frac{4 (1)}{- 12}$

Cancel the common factors.

Factor $4$ out of $- 12$ .

$m = \frac{4 \cdot 1}{4 \cdot - 3}$

Cancel the common factor.

$m = \frac{4 \cdot 1}{4 \cdot - 3}$

Rewrite the expression.

$m = \frac{1}{- 3}$

Move the negative in front of the fraction.

$m = - \frac{1}{3}$

Step 6

Find the value of $b$ using the formula for the equation of a line.

Use the formula for the equation of a line to find $b$ .

$y = m x + b$

Substitute the value of $m$ into the equation.

$y = (- \frac{1}{3}) \cdot x + b$

Substitute the value of $x$ into the equation.

$y = (- \frac{1}{3}) \cdot (7) + b$

Substitute the value of $y$ into the equation.

$0 = (- \frac{1}{3}) \cdot (7) + b$

Find the value of $b$ .

Rewrite the equation as $- \frac{1}{3} \cdot 7 + b = 0$ .

$- \frac{1}{3} \cdot 7 + b = 0$

Simplify each term.

Multiply $- \frac{1}{3} \cdot 7$ .

Multiply $7$ by $- 1$ .

$- 7 (\frac{1}{3}) + b = 0$

Combine $- 7$ and $\frac{1}{3}$ .

$\frac{- 7}{3} + b = 0$

Move the negative in front of the fraction.

$- \frac{7}{3} + b = 0$

Add $\frac{7}{3}$ to both sides of the equation.

$b = \frac{7}{3}$

Step 7

Now that the values of $m$ (slope) and $b$ (y-intercept) are known, substitute them into $y = m x + b$ to find the equation of the line.

$y = - \frac{1}{3} x + \frac{7}{3}$

Step 8

Find the Equation Using Two Points (7,0) , (-5,4)

Related Questions

Support LCMGCF.com by disabling your adblocker.