Algebra Examples

$(2, 0)$ , $(0, 3)$

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.

$m = \frac{3 - (0)}{0 - (2)}$

Step 5

Finding the slope $m$ .

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Simplify the numerator.

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Multiply $- 1$ by $0$ .

$m = \frac{3 + 0}{0 - (2)}$

Add $3$ and $0$ .

$m = \frac{3}{0 - (2)}$

Simplify the denominator.

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Multiply $- 1$ by $2$ .

$m = \frac{3}{0 - 2}$

Subtract $2$ from $0$ .

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

Move the negative in front of the fraction.

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

Step 6

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

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

$y = m x + b$

Substitute the value of $m$ into the equation.

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

Substitute the value of $x$ into the equation.

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

Substitute the value of $y$ into the equation.

$0 = (- \frac{3}{2}) \cdot (2) + b$

Find the value of $b$ .

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Rewrite the equation as $- \frac{3}{2} \cdot 2 + b = 0$ .

$- \frac{3}{2} \cdot 2 + b = 0$

Cancel the common factor of $2$ .

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Move the leading negative in $- \frac{3}{2}$ into the numerator.

$\frac{- 3}{2} \cdot 2 + b = 0$

Cancel the common factor.

$\frac{- 3}{2} \cdot 2 + b = 0$

Rewrite the expression.

$- 3 + b = 0$

Add $3$ to both sides of the equation.

$b = 3$

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.

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

Step 8