Finite Math Examples

$x = \frac{7 - y}{3}$

Step 1

Rewrite in slope-intercept form.

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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

Rewrite the equation as $\frac{7 - y}{3} = x$ .

$\frac{7 - y}{3} = x$

Step 1.3

Multiply both sides by $3$ .

$\frac{7 - y}{3} \cdot 3 = x \cdot 3$

Step 1.4

Simplify.

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Step 1.4.1

Simplify the left side.

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Step 1.4.1.1

Simplify $\frac{7 - y}{3} \cdot 3$ .

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Step 1.4.1.1.1

Cancel the common factor of $3$ .

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Step 1.4.1.1.1.1

Cancel the common factor.

$\frac{7 - y}{3} \cdot 3 = x \cdot 3$

Step 1.4.1.1.1.2

Rewrite the expression.

$7 - y = x \cdot 3$

Step 1.4.1.1.2

Reorder $7$ and $- y$ .

$- y + 7 = x \cdot 3$

Step 1.4.2

Simplify the right side.

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Step 1.4.2.1

Move $3$ to the left of $x$ .

$- y + 7 = 3 x$

Step 1.5

Solve for $y$ .

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Step 1.5.1

Subtract $7$ from both sides of the equation.

$- y = 3 x - 7$

Step 1.5.2

Divide each term in $- y = 3 x - 7$ by $- 1$ and simplify.

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Step 1.5.2.1

Divide each term in $- y = 3 x - 7$ by $- 1$ .

$\frac{- y}{- 1} = \frac{3 x}{- 1} + \frac{- 7}{- 1}$

Step 1.5.2.2

Simplify the left side.

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Step 1.5.2.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{3 x}{- 1} + \frac{- 7}{- 1}$

Step 1.5.2.2.2

Divide $y$ by $1$ .

$y = \frac{3 x}{- 1} + \frac{- 7}{- 1}$

Step 1.5.2.3

Simplify the right side.

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Step 1.5.2.3.1

Simplify each term.

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Step 1.5.2.3.1.1

Move the negative one from the denominator of $\frac{3 x}{- 1}$ .

$y = - 1 \cdot (3 x) + \frac{- 7}{- 1}$

Step 1.5.2.3.1.2

Rewrite $- 1 \cdot (3 x)$ as $- (3 x)$ .

$y = - (3 x) + \frac{- 7}{- 1}$

Step 1.5.2.3.1.3

Multiply $3$ by $- 1$ .

$y = - 3 x + \frac{- 7}{- 1}$

Step 1.5.2.3.1.4

Divide $- 7$ by $- 1$ .

$y = - 3 x + 7$

Step 2

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

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Step 2.1

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

$m = - 3$

$b = 7$

Step 2.2

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

Slope: $- 3$

y-intercept: $(0, 7)$

Slope: $- 3$

y-intercept: $(0, 7)$

Step 3