The graph below illustrates 2 intersecting lines. if a new line is drawn so that it passes through the red line at y = 0 and the blue line at x = –1, what is the slope of the new line?

0 it is a horizontal line 

To answer this, our goal here is to find the 2 points that would make our third line. So it is said in the problem that the line passes through the red line at y= 0. What value of x at y = 0 that it would lie on the red line? It must be negative 4 (-4) (check the graph to confirm) Ask the same question to the blue line but this time the value of y is to be obtained. Once you have that you will have 2 point then use this formula to get the slope: 

slope = (y2-y1)/(x2-x1) where y2 and x2 are the coordinates in the blue line. and x2 and x1, the red line.