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).
2 answers:
Step-by-step 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:
y = (-3/2)x - 6
Step-by-step 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
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