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.

Guest Jun 18, 2021

#1**+2 **

**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!**

TheOddOne Jun 18, 2021

#1**+2 **

Best Answer

**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!**

TheOddOne Jun 18, 2021