Question

The equation of the line through (2,-5) and parallel to the line x+3y-9=0is:​

Answer 1

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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