The first given equation is:
4x + 3y = 6
which can be rewritten as:
2(2x) + 3y = 6 .............> equation I
The second given equation is:
2x + 2y = 5
which can be rewritten as:
2x = 5 - 2y ........> equation II
Substitute with equation II in equation I to get the value of y as follows:
2(5-2y) + 3y = 6
10 - 4y + 3y = 6
-y = 6-10 = -4
y = 4
Substitute with the y in equation II to get x as follows:
2x = 5 - 2y
2x = 5 - 2(4)
2x = 5 - 8 = -3
x = -3/2
From the above calculations:
x = -3/2
y = 4
ANSWER
![y + 5= - \frac{9}{11} (x-3)](https://tex.z-dn.net/?f=y%20%2B%205%3D%20-%20%5Cfrac%7B9%7D%7B11%7D%20%28x-3%29)
or
![y - 4= - \frac{9}{11} (x + 8)](https://tex.z-dn.net/?f=y%20-%204%3D%20-%20%5Cfrac%7B9%7D%7B11%7D%20%28x%20%2B%208%29)
EXPLANATION
We want to find the equation in point-slope form of a line that passes through the points (3, −5) and (−8, 4).
The point-slope form is given by;
![y-y_1=m(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3Dm%28x-x_1%29)
where
![m = \frac{4 - - 5}{ - 8 - 3} = \frac{4 + 5}{ - 11} = - \frac{9}{11}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B4%20-%20-%205%7D%7B%20-%208%20-%203%7D%20%3D%20%5Cfrac%7B4%20%2B%205%7D%7B%20-%2011%7D%20%3D%20-%20%5Cfrac%7B9%7D%7B11%7D%20)
is the slope of the line.
If
![(x_1,y_1)=(3,-5)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%3D%283%2C-5%29)
The point-slope form is
![y + 5= - \frac{9}{11} (x-3)](https://tex.z-dn.net/?f=y%20%2B%205%3D%20-%20%5Cfrac%7B9%7D%7B11%7D%20%28x-3%29)
On the other hand, if
![(x_1,y_1)=( - 8,4)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%3D%28%20-%208%2C4%29)
Then the point-slope form is,
![y - 4= - \frac{9}{11} (x + 8)](https://tex.z-dn.net/?f=y%20-%204%3D%20-%20%5Cfrac%7B9%7D%7B11%7D%20%28x%20%2B%208%29)
These two equations are the same when simplified.
Answer:
Shift left 1 and down 2
Step-by-step explanation: