Algebra Examples

What is the equation of the line that passes through the point $(- 8, 3)$ and has a slope of $- \frac{1}{4}$ ?

Step 1

Find the value of $b$ using the formula for the equation of a line.

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Step 1.1

Use the formula for the equation of a line to find $b$ .

$y = m x + b$

Step 1.2

Substitute the value of $m$ into the equation.

$y = (- \frac{1}{4}) \cdot x + b$

Step 1.3

Substitute the value of $x$ into the equation.

$y = (- \frac{1}{4}) \cdot (- 8) + b$

Step 1.4

Substitute the value of $y$ into the equation.

$3 = (- \frac{1}{4}) \cdot (- 8) + b$

Step 1.5

Find the value of $b$ .

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Step 1.5.1

Rewrite the equation as $- \frac{1}{4} \cdot - 8 + b = 3$ .

$- \frac{1}{4} \cdot - 8 + b = 3$

Step 1.5.2

Simplify each term.

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Step 1.5.2.1

Cancel the common factor of $4$ .

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Step 1.5.2.1.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$\frac{- 1}{4} \cdot - 8 + b = 3$

Step 1.5.2.1.2

Factor $4$ out of $- 8$ .

$\frac{- 1}{4} \cdot (4 (- 2)) + b = 3$

Step 1.5.2.1.3

Cancel the common factor.

$\frac{- 1}{4} \cdot (4 \cdot - 2) + b = 3$

Step 1.5.2.1.4

Rewrite the expression.

$- 1 \cdot - 2 + b = 3$

Step 1.5.2.2

Multiply $- 1$ by $- 2$ .

$2 + b = 3$

Step 1.5.3

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

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Step 1.5.3.1

Subtract $2$ from both sides of the equation.

$b = 3 - 2$

Step 1.5.3.2

Subtract $2$ from $3$ .

$b = 1$

Step 2

Now that the values of $m$ (slope) and $b$ (y-intercept) are known, substitute them into $y = m x + b$ to find the equation of the line.

$y = - \frac{1}{4} x + 1$

Step 3