Finite Math Examples

$5 a - 7 b = 4$

Step 1

Solve for $y$ .

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Step 1.1

Add $7 x$ to both sides of the equation.

$5 y = 4 + 7 x$

Step 1.2

Divide each term in $5 y = 4 + 7 x$ by $5$ and simplify.

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Step 1.2.1

Divide each term in $5 y = 4 + 7 x$ by $5$ .

$\frac{5 y}{5} = \frac{4}{5} + \frac{7 x}{5}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $5$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{5 y}{5} = \frac{4}{5} + \frac{7 x}{5}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{4}{5} + \frac{7 x}{5}$

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 $\frac{4}{5}$ and $\frac{7 x}{5}$ .

$y = \frac{7 x}{5} + \frac{4}{5}$

Step 2.3

Reorder terms.

$y = \frac{7}{5} x + \frac{4}{5}$

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 $y = m x + b$ .

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

$b = \frac{4}{5}$

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: $(0, \frac{4}{5})$

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

y-intercept: $(0, \frac{4}{5})$

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

Write in $y = m x + b$ form.

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Step 4.1.1

Reorder $\frac{4}{5}$ and $\frac{7 x}{5}$ .

$y = \frac{7 x}{5} + \frac{4}{5}$

Step 4.1.2

Reorder terms.

$y = \frac{7}{5} x + \frac{4}{5}$

Step 4.2

Find the x-intercept.

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Step 4.2.1

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

$0 = \frac{7}{5} x + \frac{4}{5}$

Step 4.2.2

Solve the equation.

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Step 4.2.2.1

Rewrite the equation as $\frac{7}{5} x + \frac{4}{5} = 0$ .

$\frac{7}{5} x + \frac{4}{5} = 0$

Step 4.2.2.2

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

$\frac{7 x}{5} + \frac{4}{5} = 0$

Step 4.2.2.3

Subtract $\frac{4}{5}$ from both sides of the equation.

$\frac{7 x}{5} = - \frac{4}{5}$

Step 4.2.2.4

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$7 x = - 4$

Step 4.2.2.5

Divide each term in $7 x = - 4$ by $7$ and simplify.

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Step 4.2.2.5.1

Divide each term in $7 x = - 4$ by $7$ .

$\frac{7 x}{7} = \frac{- 4}{7}$

Step 4.2.2.5.2

Simplify the left side.

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Step 4.2.2.5.2.1

Cancel the common factor of $7$ .

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Step 4.2.2.5.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{- 4}{7}$

Step 4.2.2.5.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 4}{7}$

Step 4.2.2.5.3

Simplify the right side.

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Step 4.2.2.5.3.1

Move the negative in front of the fraction.

$x = - \frac{4}{7}$

Step 4.2.3

x-intercept(s) in point form.

x-intercept(s): $(- \frac{4}{7}, 0)$

Step 4.3

Find the y-intercept.

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Step 4.3.1

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

$y = \frac{7 (0)}{5} + \frac{4}{5}$

Step 4.3.2

Solve the equation.

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Step 4.3.2.1

Remove parentheses.

$y = \frac{7 (0)}{5} + \frac{4}{5}$

Step 4.3.2.2

Simplify $\frac{7 (0)}{5} + \frac{4}{5}$ .

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Step 4.3.2.2.1

Combine the numerators over the common denominator.

$y = \frac{7 (0) + 4}{5}$

Step 4.3.2.2.2

Simplify the expression.

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Step 4.3.2.2.2.1

Multiply $7$ by $0$ .

$y = \frac{0 + 4}{5}$

Step 4.3.2.2.2.2

Add $0$ and $4$ .

$y = \frac{4}{5}$

Step 4.3.3

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{4}{5})$

Step 4.4

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

$\begin{array}{c} x & y \\ - 2 & - 2 \\ - 2 & - 2 \end{array}$

Step 5

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

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

y-intercept: $(0, \frac{4}{5})$

$\begin{array}{c} x & y \\ - 2 & - 2 \\ - 2 & - 2 \end{array}$

Step 6