Question

What is the y-intercept of the equation of the line that is perpendicular to the line y = 3/5 x + 10 and passes through the point (15, –5)?

The equation of the line in slope-intercept form is y = -5/3x+ ? ____

Answer 1

The slope of the given line is the coefficient of x, 3/5. The slope of the perpendicular line is the negative reciprocal of that:

... m = -1/(3/5) = -5/3

The point-slope form of the equation of a line can be written as

... y = m(x -h) +k . . . . .for slope m and point (h, k)

Using the values we are given for the perpendicular line, its equation is

... y = (-5/3)(x -15) -5

Simplifying gives

... y = (-5/3)x +20

The y-intercept of the perpendicular line is 20.