Question

1. write the equation of line that has a slope of \\(\frac{1}{2}\\) and passes through the point \\((-4, 8)\\) type a response a.6.b

Explanation:

Step1: Recall point - slope form

The point - slope form of a linear equation is $y - y_1=m(x - x_1)$, where $m$ is the slope and $(x_1,y_1)$ is a point on the line. Here, $m = \frac{1}{2}$, $x_1=-4$, and $y_1 = 8$.

Step2: Substitute values into point - slope form

Substitute $m=\frac{1}{2}$, $x_1 = - 4$, and $y_1=8$ into the point - slope formula:
$y - 8=\frac{1}{2}(x - (-4))$
Simplify the right - hand side: $y - 8=\frac{1}{2}(x + 4)$

Step3: Convert to slope - intercept form (optional, but a common form)

Distribute the $\frac{1}{2}$ on the right - hand side: $y - 8=\frac{1}{2}x+2$
Add 8 to both sides of the equation: $y=\frac{1}{2}x+2 + 8$
Simplify the constant terms: $y=\frac{1}{2}x + 10$

Answer:

The equation of the line is $y=\frac{1}{2}x + 10$ (or in point - slope form $y - 8=\frac{1}{2}(x + 4)$)