For this case we have that, by definition, the equation of a line in the slope-intersection form is given by:
![y = mx + b](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20b)
Where:
m: It's the slope
b: It is the cutting point with the y axis
We have, according to the statement data that:
![m = - \frac {2} {3}](https://tex.z-dn.net/?f=m%20%3D%20-%20%5Cfrac%20%7B2%7D%20%7B3%7D)
So, the equation is of the form:
![y = - \frac {2} {3} x + b](https://tex.z-dn.net/?f=y%20%3D%20-%20%5Cfrac%20%7B2%7D%20%7B3%7D%20x%20%2B%20b)
We also have that the line intersects the "x" axis at -3, that is, the line passes through the point ![(x, y): (- 3,0)](https://tex.z-dn.net/?f=%28x%2C%20y%29%3A%20%28-%203%2C0%29)
We substitute to find "b":
![0 = -\frac {2} {3} (- 3) + b\\0 = -2 + b\\b = 2](https://tex.z-dn.net/?f=0%20%3D%20-%5Cfrac%20%7B2%7D%20%7B3%7D%20%28-%203%29%20%2B%20b%5C%5C0%20%3D%20-2%20%2B%20b%5C%5Cb%20%3D%202)
Finally, the equation is of the form:
![y = - \frac {2} {3} x + 2](https://tex.z-dn.net/?f=y%20%3D%20-%20%5Cfrac%20%7B2%7D%20%7B3%7D%20x%20%2B%202)
Answer:
![y = - \frac {2} {3} x + 2](https://tex.z-dn.net/?f=y%20%3D%20-%20%5Cfrac%20%7B2%7D%20%7B3%7D%20x%20%2B%202)
- x - y - z = - 8 ------- (1)
- 4x + 4y + 5z = 7 -------- (2)
2x + 2z = 4 --------- (3)
From (3): x + z = 2
x = 2 - z --------- (4)
Substitute (4) into (1),
- x - y - z = - 8
- (2-z) - y - z = - 8
- 2 + z - y - z = -8
- 2 - y = - 8
2 + y = 8
Therefore, y = 6
Substitute y = 6 and (4) into (2),
- 4x + 4y + 5z = 7
- 4(2 - z) + 4(6) + 5z = 7
- 8 + 4z + 24 + 5z = 7
9z + 16 = 7
9z = - 9
Therefore, z = - 9
Substitute z = - 9 into (4),
x = 2 - z
x = 2 - (-9)
x = 2 + 9
Therefore x = 11
Solution:
x = 11
y = 6
z = -9
An estimate for the percent equivalent of 7/15 is 46% i think