(Note: this answer is assuming that the equation has to be put in slope-intercept format.)
Answer:
[tex]y = \frac{1}{2} x - \frac{5}{2}[/tex]
Step-by-step explanation:
1) Let's use the point-slope formula to determine what the answer would be. To do that though, we would need two things: the slope and a point that the equation would cross through. We already have the point it would cross through, (-3,-4), based on the given information. So, in the next step, let's find the slope.
2) We know that the slope has to be parallel to the given line, [tex]y = \frac{1}{2}x - 8[/tex]. Remember that slopes that are parallel have the same slope - so, let's simply take the slope from the given equation. Since it's already in slope-intercept form, we know that the slope then must be [tex]\frac{1}{2}[/tex].
3) Finally, let's put the slope we found and the x and y values from (-3, -4) into the point-slope formula and solve:
[tex](y- (-4)) = \frac{1}{2} (x - (-3))\\y + 4 = \frac{1}{2} (x + 3))\\y + 4 = \frac{1}{2}x+ \frac{3}{2} \\y = \frac{1}{2}x + \frac{3}{2} - 4\\y = \frac{1}{2}x + \frac{3}{2} - \frac{8}{2} \\y = \frac{1}{2}x - \frac{5}{2}[/tex]
Therefore, [tex]y = \frac{1}{2}x - \frac{5}{2}[/tex] is our answer. If you have any questions, please do not hesitate to ask!
