Pre-Algebra Examples

$- 7 y = - 7 x + 49$

Step 1

Divide each term in $- 7 y = - 7 x + 49$ by $- 7$ and simplify.

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Step 1.1

Divide each term in $- 7 y = - 7 x + 49$ by $- 7$ .

$\frac{- 7 y}{- 7} = \frac{- 7 x}{- 7} + \frac{49}{- 7}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $- 7$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{- 7 y}{- 7} = \frac{- 7 x}{- 7} + \frac{49}{- 7}$

Step 1.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 7 x}{- 7} + \frac{49}{- 7}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Simplify each term.

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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.

$y = \frac{- 7 x}{- 7} + \frac{49}{- 7}$

Step 1.3.1.1.2

Divide $x$ by $1$ .

$y = x + \frac{49}{- 7}$

Step 1.3.1.2

Divide $49$ by $- 7$ .

$y = x - 7$

Step 2

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

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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

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

$m = 1$

$b = - 7$

Step 2.3

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

Slope: $1$

y-intercept: $(0, - 7)$

Slope: $1$

y-intercept: $(0, - 7)$

Step 3

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 3.1

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

$\begin{array}{c} x & y \\ 0 & - 7 \\ 1 & - 6 \end{array}$

Step 4

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

Slope: $1$

y-intercept: $(0, - 7)$

$\begin{array}{c} x & y \\ 0 & - 7 \\ 1 & - 6 \end{array}$

Step 5