Find the equation of the line which passes through (−2, 3) and the point of intersection of the lines x + 2y=0 and 2x − y − 12=0.

y = 0.794*x + 4.588

Step-by-step explanation:

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

In this case the points are:

(-2, 3) and the intersection of the lines:

x + 2y = 0

2x - y - 12  = 0

To find the intersection of those lines, we can first isolate one variable in one side of each equality, i will isolate the variable y.

y = -x/2

y = 2x - 12

Now we can write:

-x/2 = 2x - 12

Solving this we can find the value of x at which both lines intersect.

2x + x/2 = 12

(5/2)*x = 12

x = 12*(2/5) = 4.8

Now we evaluate one of the lines in that point and get:

y = -4.8/2 = -2.4

Then these lines intersect at the point (4.8, -2.4)

Now we can find the slope of our equation.

a = (-2.4 - 3)/(4.8 - (-2)) = 0.794

then we have:

y = 0.794*x + b

And we know that when x = -2, y = 3

then:

3 = 0.794*-2 + b

3 + 1.588 = b = 4.588

Then the equation is:

y = 0.794*x + 4.588

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x = 3 ± √(5+y)