Question 1203209: If the line l^1 : y=kx+b passes the point (2,3) and is perpendicular to the line y = ½x - 5, what is the equation of the line l^1?
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
The line y = (1/2)x - 5 has slope 1/2
The negative reciprocal is -2/1 aka -2.
We flip the fraction and flip the sign to get the perpendicular slope.
The mystery line has slope of m = -2
This line passes through the point (x1,y1) = (2,3)
Meaning x1 = 2 and y1 = 3.
Apply point slope form
y - y1 = m(x - x1)
y - 3 = -2(x - 2)
y - 3 = -2x + 4
y = -2x + 4 + 3
y = -2x + 7
This line has a slope of -2, which is perpendicular to the previous slope 1/2.
Also, this line goes through (2,3)
Check of the 2nd claim
y = -2x + 7
3 = -2*2 + 7
3 = -4 + 7
3 = 3
We have confirmed that (2,3) is on the line
Use of a tool like Desmos or GeoGebra is recommended to visually verify the answer.
Answer: y = -2x + 7
|
|
|
