Find the Equation Using Two Points (-7,-3) , (-2,4)

$(- 7, - 3)$ , $(- 2, 4)$

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.

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.

$m = \frac{4 - (- 3)}{- 2 - (- 7)}$

Finding the slope $m$ .

Simplify the numerator.

Multiply $- 1$ by $- 3$ .

$m = \frac{4 + 3}{- 2 - (- 7)}$

Add $4$ and $3$ .

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

Simplify the denominator.

Multiply $- 1$ by $- 7$ .

$m = \frac{7}{- 2 + 7}$

Add $- 2$ and $7$ .

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

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.

$y = (\frac{7}{5}) x + b$

Substitute the value of $x$ into the equation.

$y = (\frac{7}{5}) \cdot (- 7) + b$

Substitute the value of $y$ into the equation.

$- 3 = (\frac{7}{5}) \cdot (- 7) + b$

Find the value of $b$ .

Rewrite the equation as $\frac{7}{5} \cdot - 7 + b = - 3$ .

$\frac{7}{5} \cdot - 7 + b = - 3$

Simplify each term.

Multiply $\frac{7}{5} \cdot - 7$ .

Combine $\frac{7}{5}$ and $- 7$ .

$\frac{7 \cdot - 7}{5} + b = - 3$

Multiply $7$ by $- 7$ .

$\frac{- 49}{5} + b = - 3$

Move the negative in front of the fraction.

$- \frac{49}{5} + b = - 3$

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

Add $\frac{49}{5}$ to both sides of the equation.

$b = - 3 + \frac{49}{5}$

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$b = - 3 \cdot \frac{5}{5} + \frac{49}{5}$

Combine $- 3$ and $\frac{5}{5}$ .

$b = \frac{- 3 \cdot 5}{5} + \frac{49}{5}$

Combine the numerators over the common denominator.

$b = \frac{- 3 \cdot 5 + 49}{5}$

Simplify the numerator.

Multiply $- 3$ by $5$ .

$b = \frac{- 15 + 49}{5}$

Add $- 15$ and $49$ .

$b = \frac{34}{5}$

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.

$y = \frac{7}{5} x + \frac{34}{5}$

Find the Equation Using Two Points (-7,-3) , (-2,4)

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