Question

what is the equation of the line that passes through the point (-6, -8) and has a slope of \\(\frac{1}{2}\\)?

Explanation:

Step1: Recall point - slope form

The point - slope form of a linear equation is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope of the line.
Here, $x_1=-6$, $y_1 = - 8$ and $m=\frac{1}{2}$.

Step2: Substitute values into point - slope form

Substitute $x_1=-6$, $y_1=-8$ and $m = \frac{1}{2}$ into the point - slope formula:
$y-(-8)=\frac{1}{2}(x - (-6))$
Simplify the left - hand side and the right - hand side:
$y + 8=\frac{1}{2}(x + 6)$

Step3: Convert to slope - intercept form (optional, but to get a more standard form)

Distribute the $\frac{1}{2}$ on the right - hand side:
$y+8=\frac{1}{2}x+3$
Subtract 8 from both sides:
$y=\frac{1}{2}x+3 - 8$
$y=\frac{1}{2}x-5$

We can also leave it in point - slope form, but the slope - intercept form is a common way to present the equation of a line.

Answer:

The equation of the line is $y=\frac{1}{2}x - 5$ (or in point - slope form $y + 8=\frac{1}{2}(x + 6)$)