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