Find the Equation Using Two Points (-5,3) , (0,5)

$(- 5, 3)$ , $(0, 5)$

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.

$m = \frac{5 - (3)}{0 - (- 5)}$

Step 5

Finding the slope $m$ .

Simplify the numerator.

Multiply $- 1$ by $3$ .

$m = \frac{5 - 3}{0 - (- 5)}$

Subtract $3$ from $5$ .

$m = \frac{2}{0 - (- 5)}$

Simplify the denominator.

Multiply $- 1$ by $- 5$ .

$m = \frac{2}{0 + 5}$

Add $0$ and $5$ .

$m = \frac{2}{5}$

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.

$y = (\frac{2}{5}) x + b$

Substitute the value of $x$ into the equation.

$y = (\frac{2}{5}) \cdot (- 5) + b$

Substitute the value of $y$ into the equation.

$3 = (\frac{2}{5}) \cdot (- 5) + b$

Find the value of $b$ .

Rewrite the equation as $\frac{2}{5} \cdot - 5 + b = 3$ .

$\frac{2}{5} \cdot - 5 + b = 3$

Simplify each term.

Cancel the common factor of $5$ .

Factor $5$ out of $- 5$ .

$\frac{2}{5} \cdot (5 (- 1)) + b = 3$

Cancel the common factor.

$\frac{2}{5} \cdot (5 \cdot - 1) + b = 3$

Rewrite the expression.

$2 \cdot - 1 + b = 3$

Multiply $2$ by $- 1$ .

$- 2 + b = 3$

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

Add $2$ to both sides of the equation.

$b = 3 + 2$

Add $3$ and $2$ .

$b = 5$

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.

$y = \frac{2}{5} x + 5$

Step 8

Find the Equation Using Two Points (-5,3) , (0,5)

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