Answer:
First, let's find where the lines:
x + 2y = 0
2x - y - 12 = 0
intersect.
First, let's isolate the variable y in one side of the equalities.
y = (-x/2)
y = 2x - 12
Now we have:
-(x/2) = 2x - 12
We can solve this for x.
12 = 2*x + x/2 = 2.5*x
12/2.5 = x = 4.8
Then, replacing that value in any of the lines, we can find the value of y.
y = 2*8 - 12 = 2*4.8 - 12 = -2.4
Then those lines intersect in the point (4.8, -2.4)
Now we want to find the line that passes through the points (-2, 3) and (4.8, -2.4)
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).
Then, the slope for our line is:
a = (3 - (-2.4))/(-2 - 4.8) = -0.79
And the
y-intercept will be:
y = -0.79*x + b
when x = -2, y = 3.
3 = -2*-0.79 + b
3 - 2*0.79 = b = 1.42
The line is:
y = -0.79*x + 1.42
