Answer:
x + y = -13
Step-by-step explanation:
The equation of a line is y=mx+c
Line x+3y-9=0
Let's rearrange.
3y= -x+9
Divide both sides by 3.
3y/3 = -x/3 +9/3
y= -x/3 + 3
The gradient is the coefficient of x which is -1/3.
Therefore, m1 = -1/3
Where m1 is the gradient of the first line.
When two lines are parallel, their gradients are equal.
Therefore m1=m2
Where m2 is the gradient of the second line.
Therefore m2=-1/3
Now, we need to find c.
(2,-5)
Here, x=2, y=-5
y=mx+c
-5 = -1/3(2) + c
-5 = -2/3 + c
-5 + 2/3 = c
This can also be written as...
c = -5 +2/3
The LCM is 3.
The addition will give -13/3.
Now, let's create the equation We have m2 and c.
y = mx + c
y = -1/3(x) + (-13/3)
Take note of the signs, (+), and (-).
y = -x/3 - 13/3
Multiply both sides by 3 to remove the denominators.
(3)y = (3)-x/3 - (3)13/3
y = -x - 13
Or
x + y = -13
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