Slope interception Form

Question

Write the slope-intercept equation of the function f whose graph satisfies the given conditions, if the graph of f passes through (-12,6) and is perpendicular to the line that has an x-intercept of 4 and a y-intercept of -12

Answer 1

line with x intercept = 4 and y intercept = -12 goes through those two points (0, -12) and (4,0)

that line has slope = (-12)/(-4) = 3 = (y+12)/x

y+12 = 3x

y = 3x -12

a perpendicular line has a negative inverse slope which would be: -1/3

the perpendicular line is y=-x/3 +b solve for by plugging in the point (-12,6), x=-12, y=6

6 = -(-12)/3 + b

b = 6-4 = 2

the perpendicular line through the given point is: y=-x/3 +2 in slope intercept form

or

f(x) = (-1/3)x + 2

where -1/3 = slope, 2 = intercept