Find the Equation Using Two Points (-1,7) , (2,5)

$(- 1, 7)$ , $(2, 5)$

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.

$m = \frac{5 - (7)}{2 - (- 1)}$

Step 5

Finding the slope $m$ .

Simplify the numerator.

Multiply $- 1$ by $7$ .

$m = \frac{5 - 7}{2 - (- 1)}$

Subtract $7$ from $5$ .

$m = \frac{- 2}{2 - (- 1)}$

Simplify the denominator.

Multiply $- 1$ by $- 1$ .

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

Add $2$ and $1$ .

$m = \frac{- 2}{3}$

Move the negative in front of the fraction.

$m = - \frac{2}{3}$

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.

$y = (- \frac{2}{3}) \cdot x + b$

Substitute the value of $x$ into the equation.

$y = (- \frac{2}{3}) \cdot (- 1) + b$

Substitute the value of $y$ into the equation.

$7 = (- \frac{2}{3}) \cdot (- 1) + b$

Find the value of $b$ .

Rewrite the equation as $- \frac{2}{3} \cdot - 1 + b = 7$ .

$- \frac{2}{3} \cdot - 1 + b = 7$

Multiply $- \frac{2}{3} \cdot - 1$ .

Multiply $- 1$ by $- 1$ .

$1 (\frac{2}{3}) + b = 7$

Multiply $\frac{2}{3}$ by $1$ .

$\frac{2}{3} + b = 7$

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

Subtract $\frac{2}{3}$ from both sides of the equation.

$b = 7 - \frac{2}{3}$

To write $7$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$b = 7 \cdot \frac{3}{3} - \frac{2}{3}$

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

$b = \frac{7 \cdot 3}{3} - \frac{2}{3}$

Combine the numerators over the common denominator.

$b = \frac{7 \cdot 3 - 2}{3}$

Simplify the numerator.

Multiply $7$ by $3$ .

$b = \frac{21 - 2}{3}$

Subtract $2$ from $21$ .

$b = \frac{19}{3}$

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.

$y = - \frac{2}{3} x + \frac{19}{3}$

Step 8

Find the Equation Using Two Points (-1,7) , (2,5)

Related Questions

Support LCMGCF.com by disabling your adblocker.