Pre-Algebra Examples

$- \frac{x}{5} + \frac{y}{7} = 1$

Step 1

Solve for $y$ .

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Step 1.1

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

$\frac{y}{7} = 1 + \frac{x}{5}$

Step 1.2

Multiply both sides of the equation by $7$ .

$7 \frac{y}{7} = 7 (1 + \frac{x}{5})$

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 $7$ .

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Step 1.3.1.1.1

Cancel the common factor.

$7 \frac{y}{7} = 7 (1 + \frac{x}{5})$

Step 1.3.1.1.2

Rewrite the expression.

$y = 7 (1 + \frac{x}{5})$

Step 1.3.2

Simplify the right side.

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Step 1.3.2.1

Simplify $7 (1 + \frac{x}{5})$ .

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Step 1.3.2.1.1

Apply the distributive property.

$y = 7 \cdot 1 + 7 \frac{x}{5}$

Step 1.3.2.1.2

Multiply $7$ by $1$ .

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

Step 1.3.2.1.3

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

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

Step 1.4

Reorder $7$ and $\frac{7 x}{5}$ .

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

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.

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

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 $y = m x + b$ .

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

$b = 7$

Step 3.2

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

Slope: $\frac{7}{5}$

y-intercept: $(0, 7)$

Slope: $\frac{7}{5}$

y-intercept: $(0, 7)$

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.

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

Step 4.2

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

$\begin{array}{c} x & y \\ 0 & 7 \\ 5 & 14 \end{array}$

Step 5

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

Slope: $\frac{7}{5}$

y-intercept: $(0, 7)$

$\begin{array}{c} x & y \\ 0 & 7 \\ 5 & 14 \end{array}$

Step 6