Question

1. write the equation of the line that is parallel to $y = \frac{1}{2}x - 8$ and passes through the point (4, 10).

Explanation:

Step1: Identify parallel line slope

Parallel lines have equal slopes. The given line $y=\frac{1}{2}x - 8$ has slope $m=\frac{1}{2}$, so the target line also has $m=\frac{1}{2}$.

Step2: Substitute point into slope-intercept form

Use $y = mx + b$, substitute $x=4$, $y=10$, $m=\frac{1}{2}$:
$10 = \frac{1}{2}(4) + b$

Step3: Solve for y-intercept $b$

Calculate $\frac{1}{2}(4)=2$, then:
$10 = 2 + b$
$b = 10 - 2 = 8$

Step4: Write final line equation

Substitute $m=\frac{1}{2}$ and $b=8$ into $y=mx+b$.

Answer:

$y=\frac{1}{2}x + 8$