Question

what's an equation that the passes through (-6,4) and is parallel to y=1/2x+8
I have been trying to solve this for days now. Really need the help. Show work too.

Answer 1

By definition, if two lines share the same gradient, they are said to be parallel. So, we know for this equation, it must have a gradient of 1/2.

Now, since the point (-6, 4) passes through the line, we know it must satisfy the equation. Since we have a gradient/slope and a point, we can use the point-gradient form:

$y - y_1 = \frac{1}{2}(x - x_1)$, where $(x_1, y_1)$ represents the points being passed through.

$y - 4 = \frac{1}{2}(x + 6)$
$2y - 8 = x + 6$
$2y = x + 14$
$y = \frac{1}{2}x + 7$