Find the Equation with a Point and Slope What is the equation of the line that passes through the point (4,8) and has a slope of 3/2 ?

What is the equation of the line that passes through the point $(4, 8)$ 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.

$y = (\frac{3}{2}) \cdot (4) + b$

Substitute the value of $y$ into the equation.

$8 = (\frac{3}{2}) \cdot (4) + b$

Find the value of $b$ .

Rewrite the equation as $\frac{3}{2} \cdot 4 + b = 8$ .

$\frac{3}{2} \cdot 4 + b = 8$

Simplify each term.

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\frac{3}{2} \cdot (2 (2)) + b = 8$

Cancel the common factor.

$\frac{3}{2} \cdot (2 \cdot 2) + b = 8$

Rewrite the expression.

$3 \cdot 2 + b = 8$

Multiply $3$ by $2$ .

$6 + b = 8$

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

Subtract $6$ from both sides of the equation.

$b = 8 - 6$

Subtract $6$ from $8$ .

$b = 2$

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.

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