Algebra Examples

What is the equation of the line that passes through the point $(- 5, 2)$ and has a slope of $\frac{4}{5}$ ?

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.

$y = (\frac{4}{5}) x + b$

Step 1.3

Substitute the value of $x$ into the equation.

$y = (\frac{4}{5}) \cdot (- 5) + b$

Step 1.4

Substitute the value of $y$ into the equation.

$2 = (\frac{4}{5}) \cdot (- 5) + b$

Step 1.5

Find the value of $b$ .

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Step 1.5.1

Rewrite the equation as $\frac{4}{5} \cdot - 5 + b = 2$ .

$\frac{4}{5} \cdot - 5 + b = 2$

Step 1.5.2

Simplify each term.

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Step 1.5.2.1

Cancel the common factor of $5$ .

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Step 1.5.2.1.1

Factor $5$ out of $- 5$ .

$\frac{4}{5} \cdot (5 (- 1)) + b = 2$

Step 1.5.2.1.2

Cancel the common factor.

$\frac{4}{5} \cdot (5 \cdot - 1) + b = 2$

Step 1.5.2.1.3

Rewrite the expression.

$4 \cdot - 1 + b = 2$

Step 1.5.2.2

Multiply $4$ by $- 1$ .

$- 4 + b = 2$

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

Add $4$ to both sides of the equation.

$b = 2 + 4$

Step 1.5.3.2

Add $2$ and $4$ .

$b = 6$

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.

$y = \frac{4}{5} x + 6$

Step 3