So first you want to find the slope of the blue line.
To do this you can use the slope formula:
m = ([tex] y_{2} - y_{1} [/tex]) / ([tex] x_{2} - x_{1})
So take two points, which are already listed here.
(-5, -4) and (0, -3)
So if you input the numbers into the equation, you get:
(-4 - (-3))/(-5 - 0)
(-1) / (-5)
1/5 is the slope.
So therefore you know two key parts of the equation of the line parallel to the blue line: the slope (since they're parallel and never meet) and also a point on that line.
y = mx + b is the basic equation of a line, with m being the slope and b being the y intercept. We want to fill these in.
So we already know the slope.
So what we have in the equation right now is:
y = 1/5x + b
Since we have a point already, we can fill in that point for y and x to solve for b.
(-2, 2) is the point.
So filling it in, you get:
2 = 1/5(-2) + b
2 = -2/5 + b
b = 12/5
And then you have the equation, or:
y = 1/5x + 12/5
