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 $\frac{3}{2}$ ?

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$3 + b = - 1$

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

Subtract $3$ from both sides of the equation.

$b = - 1 - 3$

Subtract $3$ from $- 1$ .

$b = - 4$

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.

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