Algebra Examples

$m = \frac{2}{15}$ ; passes through $(5, 7)$

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.

$y = (\frac{2}{15}) x + b$

Step 1.3

Substitute the value of $x$ into the equation.

$y = (\frac{2}{15}) \cdot (5) + b$

Step 1.4

Substitute the value of $y$ into the equation.

$7 = (\frac{2}{15}) \cdot (5) + b$

Step 1.5

Find the value of $b$ .

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Step 1.5.1

Rewrite the equation as $\frac{2}{15} \cdot 5 + b = 7$ .

$\frac{2}{15} \cdot 5 + b = 7$

Step 1.5.2

Cancel the common factor of $5$ .

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Step 1.5.2.1

Factor $5$ out of $15$ .

$\frac{2}{5 (3)} \cdot 5 + b = 7$

Step 1.5.2.2

Cancel the common factor.

$\frac{2}{5 \cdot 3} \cdot 5 + b = 7$

Step 1.5.2.3

Rewrite the expression.

$\frac{2}{3} + b = 7$

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 $\frac{2}{3}$ from both sides of the equation.

$b = 7 - \frac{2}{3}$

Step 1.5.3.2

To write $7$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$b = 7 \cdot \frac{3}{3} - \frac{2}{3}$

Step 1.5.3.3

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

$b = \frac{7 \cdot 3}{3} - \frac{2}{3}$

Step 1.5.3.4

Combine the numerators over the common denominator.

$b = \frac{7 \cdot 3 - 2}{3}$

Step 1.5.3.5

Simplify the numerator.

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Step 1.5.3.5.1

Multiply $7$ by $3$ .

$b = \frac{21 - 2}{3}$

Step 1.5.3.5.2

Subtract $2$ from $21$ .

$b = \frac{19}{3}$

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.

$y = \frac{2}{15} x + \frac{19}{3}$

Step 3