Question

Through:(-4,2),parallel to y=1/4x-4

Answer 1

The equation of a line parallel to the given line and passing through the given point can be found by using the point-slope form of a linear function.
y - y₁ = m(x - x₁)  where 'm' is the slope and (x₁ , y₁) is the given point.

Now first, we need to realize that parallel lines have the same slope.  As a result, the line we are looking for will have a slope equal to our given line's slope, or 1/4

We just substitute into the equation as follows:
$y + 4 = \frac{1}{4}(x -2)$

Now you can solve for y to put this into slope-intercept form if you like:
$y= \frac{1}{4} x -4 \frac{1}{2}$