Algebra Examples

What is the equation of the line that passes through the point $(5, 2)$ and has a slope of $- \frac{6}{5}$ ?

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.

$y = (- \frac{6}{5}) \cdot x + b$

Step 1.3

Substitute the value of $x$ into the equation.

$y = (- \frac{6}{5}) \cdot (5) + b$

Step 1.4

Substitute the value of $y$ into the equation.

$2 = (- \frac{6}{5}) \cdot (5) + b$

Step 1.5

Find the value of $b$ .

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Step 1.5.1

Rewrite the equation as $- \frac{6}{5} \cdot 5 + b = 2$ .

$- \frac{6}{5} \cdot 5 + b = 2$

Step 1.5.2

Cancel the common factor of $5$ .

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Step 1.5.2.1

Move the leading negative in $- \frac{6}{5}$ into the numerator.

$\frac{- 6}{5} \cdot 5 + b = 2$

Step 1.5.2.2

Cancel the common factor.

$\frac{- 6}{5} \cdot 5 + b = 2$

Step 1.5.2.3

Rewrite the expression.

$- 6 + b = 2$

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 $6$ to both sides of the equation.

$b = 2 + 6$

Step 1.5.3.2

Add $2$ and $6$ .

$b = 8$

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.

$y = - \frac{6}{5} x + 8$

Step 3