We have the equation of a line that is y=-4x+2.
A perpendicular line will have a slope that is the negative reciprocal of the original slope.
Then, as our original line has a slope of m=-4 (the factor that multiplies the x in slope-intercept form), the negative reciprocal is:
[tex]m_2=-\frac{1}{m_1}=-\frac{1}{-4}=\frac{1}{4}[/tex]Then, any line that has a slope m=1/4 is perpendicular to the original line.
From the options, the only one that satisfies this condition is Option 4: y=1/4*x+5.
Answer: 4)y=1/4x+5
