Algebra Examples

$\frac{x}{5} = \frac{y}{3}$

Step 1

Solve for $y$ .

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Step 1.1

Rewrite the equation as $\frac{y}{3} = \frac{x}{5}$ .

$\frac{y}{3} = \frac{x}{5}$

Step 1.2

Multiply both sides of the equation by $3$ .

$3 \frac{y}{3} = 3 \frac{x}{5}$

Step 1.3

Simplify both sides of the equation.

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Step 1.3.1

Simplify the left side.

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Step 1.3.1.1

Cancel the common factor of $3$ .

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Step 1.3.1.1.1

Cancel the common factor.

$3 \frac{y}{3} = 3 \frac{x}{5}$

Step 1.3.1.1.2

Rewrite the expression.

$y = 3 \frac{x}{5}$

Step 1.3.2

Simplify the right side.

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Step 1.3.2.1

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

$y = \frac{3 x}{5}$

Step 2

Rewrite in slope-intercept form.

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Step 2.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 2.2

Reorder terms.

$y = \frac{3}{5} x$

Step 3

Use the slope-intercept form to find the slope and y-intercept.

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Step 3.1

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = \frac{3}{5}$

$b = 0$

Step 3.2

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $\frac{3}{5}$

y-intercept: $(0, 0)$

Slope: $\frac{3}{5}$

y-intercept: $(0, 0)$

Step 4

Any line can be graphed using two points. Select two $x$ values, and plug them into the equation to find the corresponding $y$ values.

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Step 4.1

Reorder terms.

$y = \frac{3}{5} x$

Step 4.2

Create a table of the $x$ and $y$ values.

$\begin{array}{c} x & y \\ 0 & 0 \\ 5 & 3 \end{array}$

Step 5

Graph the line using the slope and the y-intercept, or the points.

Slope: $\frac{3}{5}$

y-intercept: $(0, 0)$

$\begin{array}{c} x & y \\ 0 & 0 \\ 5 & 3 \end{array}$

Step 6