Answer:
D
Step-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.
