Question

find the equation of the line that is parallel to $y = \frac{3}{4}x + 2$ and contains the point (8,16). $y = \frac{?}{\square}x + \square$

Explanation:

Step1: Identify parallel slope

Parallel lines have equal slopes. The given line $y = \frac{3}{4}x + 2$ has slope $\frac{3}{4}$, so the new line also has $m = \frac{3}{4}$.

Step2: Substitute point into slope-intercept form

Use $y = mx + b$, substitute $x=8$, $y=16$, $m=\frac{3}{4}$:
$$16 = \frac{3}{4}(8) + b$$

Step3: Solve for y-intercept $b$

Calculate $\frac{3}{4}(8)=6$, then:
$$16 = 6 + b$$
$$b = 16 - 6 = 10$$

Step4: Write final line equation

Combine slope and y-intercept:
$$y = \frac{3}{4}x + 10$$

Answer:

$y = \frac{3}{4}x + 10$