Pre-Algebra Examples

$m = \frac{7}{8}$ , $(3, - 7)$

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.

$y = (\frac{7}{8}) x + b$

Step 1.3

Substitute the value of $x$ into the equation.

$y = (\frac{7}{8}) \cdot (3) + b$

Step 1.4

Substitute the value of $y$ into the equation.

$- 7 = (\frac{7}{8}) \cdot (3) + b$

Step 1.5

Find the value of $b$ .

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Step 1.5.1

Rewrite the equation as $\frac{7}{8} \cdot 3 + b = - 7$ .

$\frac{7}{8} \cdot 3 + b = - 7$

Step 1.5.2

Multiply $\frac{7}{8} \cdot 3$ .

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Step 1.5.2.1

Combine $\frac{7}{8}$ and $3$ .

$\frac{7 \cdot 3}{8} + b = - 7$

Step 1.5.2.2

Multiply $7$ by $3$ .

$\frac{21}{8} + b = - 7$

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 $\frac{21}{8}$ from both sides of the equation.

$b = - 7 - \frac{21}{8}$

Step 1.5.3.2

To write $- 7$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$b = - 7 \cdot \frac{8}{8} - \frac{21}{8}$

Step 1.5.3.3

Combine $- 7$ and $\frac{8}{8}$ .

$b = \frac{- 7 \cdot 8}{8} - \frac{21}{8}$

Step 1.5.3.4

Combine the numerators over the common denominator.

$b = \frac{- 7 \cdot 8 - 21}{8}$

Step 1.5.3.5

Simplify the numerator.

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Step 1.5.3.5.1

Multiply $- 7$ by $8$ .

$b = \frac{- 56 - 21}{8}$

Step 1.5.3.5.2

Subtract $21$ from $- 56$ .

$b = \frac{- 77}{8}$

Step 1.5.3.6

Move the negative in front of the fraction.

$b = - \frac{77}{8}$

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.

$y = \frac{7}{8} x - \frac{77}{8}$

Step 3