Question

What is an equation of the line that passes through the point (4,−3) and is perpendicular to the line 4x+y=3

Answer 1

`y = (1)/(4) x - 4`

Explanation:

Slope intercept form of line equation is y = mx + b, m = slope, b = y-intercept

Slope of line perpendicular to y =m x + b will have slope - (1/m)

4x+y=3 can be re-written as
y = -4x + 3

Slope = -4

Slope of line perpendicular to this line is - (1/-4) = 1/4

Line equation: y = (1/4) x + b

Plug in x, y values from given point into this line equation to find b
-3 = 1/4 x 4 + b

-3 = 1 + b

-3 -1 = b

b = -4

So equation of perpendicular line is y = (1/4)x - 4