Algebra Examples

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

Step 1

Find the slope of the line between $(0, 2)$ and $(3, 3)$ using $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ , which is the change of $y$ over the change of $x$ .

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Step 1.1

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 1.2

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 1.3

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

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

Step 1.4

Simplify.

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Step 1.4.1

Simplify the numerator.

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Step 1.4.1.1

Multiply $- 1$ by $2$ .

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

Step 1.4.1.2

Subtract $2$ from $3$ .

$m = \frac{1}{3 - (0)}$

Step 1.4.2

Simplify the denominator.

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Step 1.4.2.1

Multiply $- 1$ by $0$ .

$m = \frac{1}{3 + 0}$

Step 1.4.2.2

Add $3$ and $0$ .

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

Step 2

Use the slope $\frac{1}{3}$ and a given point $(0, 2)$ to substitute for $x_{1}$ and $y_{1}$ in the point-slope form $y - y_{1} = m (x - x_{1})$ , which is derived from the slope equation $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (2) = \frac{1}{3} \cdot (x - (0))$

Step 3

Simplify the equation and keep it in point-slope form.

$y - 2 = \frac{1}{3} \cdot (x + 0)$

Step 4

Solve for $y$ .

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Step 4.1

Simplify $\frac{1}{3} \cdot (x + 0)$ .

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Step 4.1.1

Add $x$ and $0$ .

$y - 2 = \frac{1}{3} \cdot x$

Step 4.1.2

Combine $\frac{1}{3}$ and $x$ .

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

Step 4.2

Add $2$ to both sides of the equation.

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

Step 5

Reorder terms.

$y = \frac{1}{3} x + 2$

Step 6

List the equation in different forms.

Slope-intercept form:

$y = \frac{1}{3} x + 2$

Point-slope form:

$y - 2 = \frac{1}{3} \cdot (x + 0)$

Step 7