Parallel to y + 8x = 4 through (3, 4); slope-intercept form

y = - 8x + 28

Step-by-step explanation:

The equation of a line in slope - intercept form is

y = mx + c (m is the slope and c the y - intercept)

Rearrange y + 8x = 4 into this form

Subtract 8x from both sides

y = - 8x + 4 ← in slope - intercept form

with slope m = - 8

Parallel lines have equal slopes, thus

y = - 8x + c ← is the partial equation

To find c substitute (3, 4) into the partial equation

4 = - 24 + c ⇒ c = 4 + 24 = 28

y = - 8x + 28 ← equation of line