Two perpendicular lines intersect on the -axis. The equation of one line is y- 4x-6=0. Determine the equation of the other line.

y = x + 6 or y = x - 0.375

Step-by-step explanation:

For 2 lines to be perpendicular, their slopes must be negative reciprocals. In order to find the perpendicular of y - 4x - 6 = 0:

SLOPE INTERCEPT FORM: y = 4x + 6

SLOPE OF LINE A: m=4

SLOPE OF LINE B (the one you are looking for): m=

Since I don't know if you meant that they intercept on the x or y axis I will do both.

y-axis

y-6=(x-0)

y = x+6

x-axis

y-0=(x-1.5)

y=x-0.375

let soccer = x and golf = y

part a

1st equation: x + y = 125

2nd equation: x = y +45

part b

replace x in the 1st equation with the 2nd one:

y + 45 + y = 125

simplify:

2y + 45 = 125

subtract 45 from each side:

2y = 80

divide both sides by 2:

y = 80/2

y = 40

she plays golf for 40 minutes.

part c

no because she plays soccer for 45 minutes longer than golf 40 +45 =   85 minutes, not 80 minutes.