Precalculus Examples

$3 x + 2 y = 5$

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

Subtract $3 x$ from both sides of the equation.

$2 y = 5 - 3 x$

Step 1.3

Divide each term in $2 y = 5 - 3 x$ by $2$ and simplify.

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Step 1.3.1

Divide each term in $2 y = 5 - 3 x$ by $2$ .

$\frac{2 y}{2} = \frac{5}{2} + \frac{- 3 x}{2}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $2$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{5}{2} + \frac{- 3 x}{2}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{5}{2} + \frac{- 3 x}{2}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Move the negative in front of the fraction.

$y = \frac{5}{2} - \frac{3 x}{2}$

Step 1.4

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

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Step 1.4.1

Reorder $\frac{5}{2}$ and $- \frac{3 x}{2}$ .

$y = - \frac{3 x}{2} + \frac{5}{2}$

Step 1.4.2

Reorder terms.

$y = - (\frac{3}{2} x) + \frac{5}{2}$

Step 1.4.3

Remove parentheses.

$y = - \frac{3}{2} x + \frac{5}{2}$

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 $y = m x + b$ .

$m = - \frac{3}{2}$

$b = \frac{5}{2}$

Step 2.2

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

Slope: $- \frac{3}{2}$

y-intercept: $(0, \frac{5}{2})$

Slope: $- \frac{3}{2}$

y-intercept: $(0, \frac{5}{2})$

Step 3