A line described by the equation -4x + Y = 2 is graphed on a coordinate plane. Which equation describes the graph of a line passing through the point (-1, 3) and parallel to the line described by -4x + y = 2?

Answer:DStep-by-step explanation:We know that parallel lines have equal slopes.Let's transform the given equation to the form y = mx + b to find the slope (m is the slope). Shown below:[tex]-4x+y=2\\y=4x+2[/tex]So the slope is 4. Hence the parallel line will have a slope of 4.Now we can write the equation of the parallel line as :[tex]y=4x+c[/tex]Since the line goes through (-1,3), we can plug in -1 into x and 3 into y to find out c:[tex]y=4x+c\\3=4(-1)+c\\3=-4+c\\3+4=c\\c=7[/tex]Now we know both m and c, so the equation of the parallel line is:[tex]y=4x+7[/tex]Answer choice D is right.