Find the Equation with a Point and Slope What is the equation of the line that passes through the point (-2,1) and has a slope of 3/2 ?

What is the equation of the line that passes through the point $(- 2, 1)$ and has a slope of $\frac{3}{2}$ ?

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.

$y = (\frac{3}{2}) x + b$

Substitute the value of $x$ into the equation.

$y = (\frac{3}{2}) \cdot (- 2) + b$

Substitute the value of $y$ into the equation.

$1 = (\frac{3}{2}) \cdot (- 2) + b$

Find the value of $b$ .

Rewrite the equation as $\frac{3}{2} \cdot - 2 + b = 1$ .

$\frac{3}{2} \cdot - 2 + b = 1$

Simplify each term.

Cancel the common factor of $2$ .

Factor $2$ out of $- 2$ .

$\frac{3}{2} \cdot (2 (- 1)) + b = 1$

Cancel the common factor.

$\frac{3}{2} \cdot (2 \cdot - 1) + b = 1$

Rewrite the expression.

$3 \cdot - 1 + b = 1$

Multiply $3$ by $- 1$ .

$- 3 + b = 1$

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

Add $3$ to both sides of the equation.

$b = 1 + 3$

Add $1$ and $3$ .

$b = 4$

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.

$y = \frac{3}{2} x + 4$

Step 3