Question

which equation represents the line that passes through the point $(-2,2)$ and is parallel to $y = \frac{1}{2}x + 8$?$circ$ $y = \frac{1}{2}xLXB0circ$ $y = \frac{1}{2}x + 3$$circ$ $y = -2x + 3$

Explanation:

Step1: Identify parallel line slope

Parallel lines have equal slopes. For $y = \frac{1}{2}x + 8$, the slope $m = \frac{1}{2}$. So the target line has $m = \frac{1}{2}$.

Step2: Use point-slope form

Point-slope formula: $y - y_1 = m(x - x_1)$. Substitute $m = \frac{1}{2}$, $x_1=-2$, $y_1=2$:
$y - 2 = \frac{1}{2}(x - (-2))$

Step3: Simplify to slope-intercept form

Simplify the right-hand side:
$y - 2 = \frac{1}{2}(x + 2)$
$y - 2 = \frac{1}{2}x + 1$
Add 2 to both sides:
$y = \frac{1}{2}x + 3$

Step4: Match with options

The derived equation matches one of the given options.

Answer:

y = 1/2x + 3