Andrea, this is the solution to this exercise:
Step 1. As you can see, the point of intersection of the red line and the blue line is
(-2, 1)
Step 2. Now, let's find the equation for each of the lines, as follows:
Blue line: We have two points (-3, 4) and (-1, -2)
The general equation of a line is:
y = mx + b, where m is the slope and b is the y-intercept.
m (slope) = (-2 - 4)/ (-1 - -3)
m = -6/2
m = -3
Let's calculate b, using (-1, -2):
-2 = -3 * -1 + b
-2 = 3 + b
-2 - 3 = b
b = -5
In consequence, the equation of the blue line is:
y = -3x - 5
Step 3: Let's find the equation of the red line, this way:
Red line, we have two points: (-4, 0) and (4, 4)
The general equation of a line is:
y = mx + b, where m is the slope and b is the y-intercept.
m (slope) = (4 -0)/ (4 - -4)
m = 4/8
m = 1/2 (Simplifying)
Let's calculate b, using (4, 4):
4 = 1/2 * 4 + b
4 = 2 + b
4 - 2 = b
b = 2
Therefore, the equation of the red line is:
y = 1/2x + 2