Precalculus Examples

$- 3 x + 5 y - 8 = 0$

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

Move all terms not containing $y$ to the right side of the equation.

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Step 1.2.1

Add $3 x$ to both sides of the equation.

$5 y - 8 = 3 x$

Step 1.2.2

Add $8$ to both sides of the equation.

$5 y = 3 x + 8$

Step 1.3

Divide each term in $5 y = 3 x + 8$ by $5$ and simplify.

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Step 1.3.1

Divide each term in $5 y = 3 x + 8$ by $5$ .

$\frac{5 y}{5} = \frac{3 x}{5} + \frac{8}{5}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $5$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{5 y}{5} = \frac{3 x}{5} + \frac{8}{5}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{3 x}{5} + \frac{8}{5}$

Step 1.4

Reorder terms.

$y = \frac{3}{5} x + \frac{8}{5}$

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 $y = m x + b$ .

$m = \frac{3}{5}$

$b = \frac{8}{5}$

Step 2.2

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

Slope: $\frac{3}{5}$

y-intercept: $(0, \frac{8}{5})$

Slope: $\frac{3}{5}$

y-intercept: $(0, \frac{8}{5})$

Step 3