Write an equation of the line that passes through (-4,1) and is perpendicular to the line y=2x+3.

Question

I really need help with this

Answer 1

Do you understand that lines that are perpendicular have slopes that are negative reciprocals (assuming the lines are not horizontal and vertical). That means if a line has a slope of 7, a line perpendicular to it has a slope of -1/7. Similarly a line with a slope of -3/5 will have perpendicular lines with a slope of 5/3.

For this problem the slope of the given line is 2 (y=mx+b), so the slope of any line perpendicular to it will have a slope of -1/2. But that perpendicular must pass through (-4,1). You can use either point-slope or slope-intercept to find the equation of the required line.

y-1=-1/2(x+4)

or

1=-1/2(-4) + b

Your choice.

Check it out here:

desmos.com/calculator/63rpawousu

Use the slider on "b" to make the green dashed line coincide with the black line.