Question

Part A: Write an equation of a line that is perpendicular to the line y = 2/3x + 5 and passes through the point (4, 0).

Part B: Explain how you determine the equation in 3-4 sentences using at least 6 of the words below.
Slope
y-intercept
x-intercept
perpendicular
opposite
reciprocal
substituted/substitution
slope-intercept
ordered pair

Answer 1

Explanation:

First you need to make a line perpendicular to y=2/3x+5. To do that you have to know that, if we use y=ax+b, a1*a2=-1. That is if a1 and a2 are perpendicular. So we get 2/3*a2=-1. -1/ 2/3=a2. a2=-1.5. We get y=-1.5x+b. Fill in (4,0) on y=-1.5x+b abd we get 0=-1.5(4)+b. b=6

Answer 2

y = (-3/2)x - 6

Explanation:

slope of the line y= 2/3x + 5

slope = 2/3

for two perpendicular lines

slope1*slope2 = -1

so, slope2 = (-1)*(3/2) = -3/2

hence for it to pass (4,0)

slope2=(y2 - y1)/(x2 - x1)

-3/2 = (y - 0)/(x - 4)

cross multiplying

-3x -12 = 2y

the equation of the line is

y = (-3/2)x - 6