Precalculus Examples

$- 5 x + 7 y - 1 = 0$

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 $5 x$ to both sides of the equation.

$7 y - 1 = 5 x$

Step 1.2.2

Add $1$ to both sides of the equation.

$7 y = 5 x + 1$

Step 1.3

Divide each term in $7 y = 5 x + 1$ by $7$ and simplify.

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Step 1.3.1

Divide each term in $7 y = 5 x + 1$ by $7$ .

$\frac{7 y}{7} = \frac{5 x}{7} + \frac{1}{7}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $7$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{7 y}{7} = \frac{5 x}{7} + \frac{1}{7}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{5 x}{7} + \frac{1}{7}$

Step 1.4

Reorder terms.

$y = \frac{5}{7} x + \frac{1}{7}$

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 $y = m x + b$ .

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

$b = \frac{1}{7}$

Step 2.2

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

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

y-intercept: $(0, \frac{1}{7})$

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

y-intercept: $(0, \frac{1}{7})$

Step 3