We want to know if the blue line is parallel to the red line. To do so, remember that nonvertical parallel lines have the same slope. Because these lines intersect they do not have the same slopes, and therefore are not parallel. However, let's examine this further. Recall the formula for the slope of a line.
m = y_2-y_1/x_2-x_1
Now we can find the slope of each line. We will start by substituting x_1= - 1, y_1= 0, x_2= 1, and y_2= - 2 into the above formula to calculate the slope for the blue line. Let's do it!
The slope of the blue line is equal to - 1. To find the slope of red line, we can substitute x_1= - 1, y_1= 3, x_2= 1, and y_2= - 1 into the slope formula.
