Write an equation in slope-intercept form for the line that passes through the given point and is parallel to the graph of each equation.

Question

(1, -3), y = -4x - 1 and (-4, 2), y = x + 3

Answer 1

Slope intercept form is y = mx + b where m = gradient and b = y intercept.

equation (1) is y = -4x - 1 is already in this form, m=-4 and b = -1

perpendicular lines m1 x m2 = -1 (i.e. each slope is negative inverse of the other)

-4 x m2 = -1 => m2 = 1/4

equation of perpendicular line is y = 1/4 x + c

substitute point values (1, -3) to find c:

-3 = 1/4 (1) + c => -3 - 1/4 = c => c = -13/4

hence required equation is y = 1/4 x - 13/4 which is equivalent to 4y = x - 13

now do the same with equation (2) y = x + 3 where m = 1 and b = ?

m1 x m2 = -1

1 x m2 = -1 => m2 = ?

required equation of perpendicular line is therefore y =