Question

write an equation of the line that passes through the given point and has the given slope: (4,2); m = \\(\frac{1}{2}\\) \\(y = \frac{1}{2}x\\) \\(y = \frac{1}{2}x + 1\\) \\(y = -\frac{1}{2}x\\) \\(y = \frac{1}{2}x - 1\\)

Explanation:

Step1: Use point-slope form

The point-slope formula is $y - y_1 = m(x - x_1)$, where $(x_1, y_1)=(4,2)$ and $m=\frac{1}{2}$.
$y - 2 = \frac{1}{2}(x - 4)$

Step2: Simplify to slope-intercept form

Expand and isolate $y$:
$y - 2 = \frac{1}{2}x - 2$
$y = \frac{1}{2}x - 2 + 2$
$y = \frac{1}{2}x$

Answer:

A. $y = \frac{1}{2}x$