Question

find the equation of the line that is parallel to the line y=15x and contains the point (1,-4)
y=


find the distance d (p_1, and p_2) between the points p_1 and p_2
p_1=(-2,1)
p_2=(1,4)

Answer 1

(1) The slope must be 15. To pass through (1,-4), it must be the equation
y + 4 = 15 (x - 1)
That can be rewritten in standard form as
y = 15x -19

(2) (distance)^2 = (y2-y1)^2 +(x2-x1)^2
=(4-1)^2 + [1 - (-3)]^2 = 9 + 16 = 25
distance = 5

Answer 2

Write the equation in slope intercept form of a line that is perpendicular to y=-15x-7 but goes through the point (0,2).