Answer: 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
