Line l_1 represents the graph of 3x + 4y = -14. Line l_2 passes through the point (-5,7), and is perpendicular to line l_1. If line l_2 represents the graph of y=mx +b, then find m+b.
Answer:
44/3
Solution:
Hi Guest! Sorry for the late help
Let's get \(\mathrm{Line_1}\) into standard form first, yeah?
\(\mathrm{Line_1}\) =
3x+4y=-14
4y=-3x-14
y=-3x/4 -7/2
So now that \(\mathrm{Line_1}\) is now happily in standard form, let's start looking for \(\mathrm{Line_2}\)'s equation.
First, let's find the slope.
To find a perpendicular line, you have to take the opposite reciprocal of \(\mathrm{Line_1}\)'s slope, which is -3/4.
So \(\mathrm{Line_2}\)'s new slope is 4/3.
What we have so far for \(\mathrm{Line_2}\): y=4/3 x + b
Now we need to find b.
We can do that by plugging in (-5,7), a point on the line, into x and y in the partially done equation for \(\mathrm{Line_2}\).
y = 4/3 x + b <-- before plugging in
7 = 4/3 * -5 + b <-- after plugging in
7 = -20/3 + b <-- simplifying
41/3 = b <-- even more simplifying
b = 41/3 <-- just flipping it nothing here to see
So we have the full equation for \(\mathrm{Line_2}\), or, y = 4/3 x + 41/3.
From here, we look at the question again. What is it asking for?
"find m+b"
m = 4/3, and b= 41/3.
Hence, the answer is 44/3.
=^-^=
If you find a mistake, please let me know in the replies!
Answer:
44/3
Solution:
Hi Guest! Sorry for the late help
Let's get \(\mathrm{Line_1}\) into standard form first, yeah?
\(\mathrm{Line_1}\) =
3x+4y=-14
4y=-3x-14
y=-3x/4 -7/2
So now that \(\mathrm{Line_1}\) is now happily in standard form, let's start looking for \(\mathrm{Line_2}\)'s equation.
First, let's find the slope.
To find a perpendicular line, you have to take the opposite reciprocal of \(\mathrm{Line_1}\)'s slope, which is -3/4.
So \(\mathrm{Line_2}\)'s new slope is 4/3.
What we have so far for \(\mathrm{Line_2}\): y=4/3 x + b
Now we need to find b.
We can do that by plugging in (-5,7), a point on the line, into x and y in the partially done equation for \(\mathrm{Line_2}\).
y = 4/3 x + b <-- before plugging in
7 = 4/3 * -5 + b <-- after plugging in
7 = -20/3 + b <-- simplifying
41/3 = b <-- even more simplifying
b = 41/3 <-- just flipping it nothing here to see
So we have the full equation for \(\mathrm{Line_2}\), or, y = 4/3 x + 41/3.
From here, we look at the question again. What is it asking for?
"find m+b"
m = 4/3, and b= 41/3.
Hence, the answer is 44/3.
=^-^=
If you find a mistake, please let me know in the replies!