Pre-Algebra Examples

$37 n - 2.7$

Step 1

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

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Step 1.1

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 1.2

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

$m = 37$

$b = - 2.7$

Step 1.3

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

Slope: $37$

y-intercept: $(0, - 2.7)$

Slope: $37$

y-intercept: $(0, - 2.7)$

Step 2

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 2.1

Find the x-intercept.

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Step 2.1.1

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = 37 x - 2.7$

Step 2.1.2

Solve the equation.

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Step 2.1.2.1

Rewrite the equation as $37 x - 2.7 = 0$ .

$37 x - 2.7 = 0$

Step 2.1.2.2

Add $2.7$ to both sides of the equation.

$37 x = 2.7$

Step 2.1.2.3

Divide each term in $37 x = 2.7$ by $37$ and simplify.

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Step 2.1.2.3.1

Divide each term in $37 x = 2.7$ by $37$ .

$\frac{37 x}{37} = \frac{2.7}{37}$

Step 2.1.2.3.2

Simplify the left side.

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Step 2.1.2.3.2.1

Cancel the common factor of $37$ .

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Step 2.1.2.3.2.1.1

Cancel the common factor.

$\frac{37 x}{37} = \frac{2.7}{37}$

Step 2.1.2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{2.7}{37}$

Step 2.1.2.3.3

Simplify the right side.

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Step 2.1.2.3.3.1

Divide $2.7$ by $37$ .

$x = 0.0\overline{729}$

Step 2.1.3

x-intercept(s) in point form.

x-intercept(s): $(0.0\overline{729}, 0)$

Step 2.2

Find the y-intercept.

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Step 2.2.1

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = 37 (0) - 2.7$

Step 2.2.2

Solve the equation.

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Step 2.2.2.1

Remove parentheses.

$y = 37 (0) - 2.7$

Step 2.2.2.2

Simplify $37 (0) - 2.7$ .

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Step 2.2.2.2.1

Multiply $37$ by $0$ .

$y = 0 - 2.7$

Step 2.2.2.2.2

Subtract $2.7$ from $0$ .

$y = - 2.7$

Step 2.2.3

y-intercept(s) in point form.

y-intercept(s): $(0, - 2.7)$

Step 2.3

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

$\begin{array}{c} x & y \\ 0 & - 2.7 \\ 0 & - 2.7 \end{array}$

Step 3

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

Slope: $37$

y-intercept: $(0, - 2.7)$

$\begin{array}{c} x & y \\ 0 & - 2.7 \\ 0 & - 2.7 \end{array}$

Step 4