Find the Equation with a Point and Slope What is the equation of the line that passes through the point (5,-2) and has a slope of 6/5 ?

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.

Use the formula for the equation of a line to find $b$ .

$y = m x + b$

Substitute the value of $m$ into the equation.

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

Substitute the value of $x$ into the equation.

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

Substitute the value of $y$ into the equation.

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

Find the value of $b$ .

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

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

Cancel the common factor of $5$ .

Cancel the common factor.

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

Rewrite the expression.

$6 + b = - 2$

Move all terms not containing $b$ to the right side of the equation.

Subtract $6$ from both sides of the equation.

$b = - 2 - 6$

Subtract $6$ from $- 2$ .

$b = - 8$

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