Line $1$ represents the graph of $3x + 4y = -14$. Line $2$ passes through the point $(-5,7)$, and is perpendicular to line $1$. If line $2$ represents the graph of $y=mx +b$, then find $m+b$.

15

Step-by-step explanation:

First, solve for Line 1

3x + 4y = -14

move the x to the right of the equation

4y = -3x - 14

divide the whole equation by 4

y = -3/4x - 14/4

Line 1 is y = -3/4x - 7/2

Then, solve for Line 2

Since Line 2 is perpendicular, change the sign of the slope of Line 1 and then get the reciprocal of that.

-3/4 to 3/4 to 4/3

4/3 is the slope of Line 2.

Now, we want to find what the b of the equation is, so we can plug in our x (-5) and our y (7) into the y=mx+b equation to find b. The 4/3 is the m or the slope.

y = mx + b

plug in the y, m, and x into the equation

7 = (4/3)(-5) + b

multiply the m and x together

7 = -20/3 + b

add 20/3 to both sides so it will cancel out on the right of the equation and be added to the 7 on the left of the equation

41/3 = b

So, m = 4/3 and b = 41/3

Add them together and you get 45/3 or 15.

I hope this helped!