Answer:
The line that meets these conditions is y = 1.5x - 2.5
If you want to use fractions, it would be y = 3x/2 - 5/2
Step-by-step explanation:
To get a line perpendicular to y = -(2/3)x + 1, We can start by finding its slope. That's easy enough as a perpendicular slope is the negative reciprocal of the given one. As this has a slope of -2/3, our new slope has to be 3/2, or 1.5
All we need to do then is express that rate of change relative to the given point (-1, -4). We can do this by expanding the classic equation:
Δy = sΔx
We can write that as such:
y - (-4) = 1.5(x - (-1))
y + 4 = 1.5(x + 1)
y + 4 = 1.5x + 1.5
y = 1.5x + 1.5 - 4
y = 1.5x - 2.5
Or if you want to express those numbers as fractions, it would be y = 3x/2 - 5/2.
To make sure the answer's correct, we can simply plug -1 in as the x value, and see if we get y = -4:
y = 3(-1) / 2 - 5/2
y = -3 / 2 - 5 / 2
y = -8 / 2
y = -4
So we know that our answer is correct (assuming that the slope is correct, which it is - a perpendicular line always has the negative reciprocal of the other line's slope).
