Algebra Examples

$m = - \frac{7}{16}$ , $(- 8, 16)$

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.

$y = (- \frac{7}{16}) \cdot x + b$

Step 1.3

Substitute the value of $x$ into the equation.

$y = (- \frac{7}{16}) \cdot (- 8) + b$

Step 1.4

Substitute the value of $y$ into the equation.

$16 = (- \frac{7}{16}) \cdot (- 8) + b$

Step 1.5

Find the value of $b$ .

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Step 1.5.1

Rewrite the equation as $- \frac{7}{16} \cdot - 8 + b = 16$ .

$- \frac{7}{16} \cdot - 8 + b = 16$

Step 1.5.2

Simplify each term.

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Step 1.5.2.1

Cancel the common factor of $8$ .

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Step 1.5.2.1.1

Move the leading negative in $- \frac{7}{16}$ into the numerator.

$\frac{- 7}{16} \cdot - 8 + b = 16$

Step 1.5.2.1.2

Factor $8$ out of $16$ .

$\frac{- 7}{8 (2)} \cdot - 8 + b = 16$

Step 1.5.2.1.3

Factor $8$ out of $- 8$ .

$\frac{- 7}{8 \cdot 2} \cdot (8 \cdot - 1) + b = 16$

Step 1.5.2.1.4

Cancel the common factor.

$\frac{- 7}{8 \cdot 2} \cdot (8 \cdot - 1) + b = 16$

Step 1.5.2.1.5

Rewrite the expression.

$\frac{- 7}{2} \cdot - 1 + b = 16$

Step 1.5.2.2

Combine $\frac{- 7}{2}$ and $- 1$ .

$\frac{- 7 \cdot - 1}{2} + b = 16$

Step 1.5.2.3

Multiply $- 7$ by $- 1$ .

$\frac{7}{2} + b = 16$

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 $\frac{7}{2}$ from both sides of the equation.

$b = 16 - \frac{7}{2}$

Step 1.5.3.2

To write $16$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$b = 16 \cdot \frac{2}{2} - \frac{7}{2}$

Step 1.5.3.3

Combine $16$ and $\frac{2}{2}$ .

$b = \frac{16 \cdot 2}{2} - \frac{7}{2}$

Step 1.5.3.4

Combine the numerators over the common denominator.

$b = \frac{16 \cdot 2 - 7}{2}$

Step 1.5.3.5

Simplify the numerator.

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Step 1.5.3.5.1

Multiply $16$ by $2$ .

$b = \frac{32 - 7}{2}$

Step 1.5.3.5.2

Subtract $7$ from $32$ .

$b = \frac{25}{2}$

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.

$y = - \frac{7}{16} x + \frac{25}{2}$

Step 3