In xy-coordinate plane, the graph of x=y^2 -4 intersects line A at (0,p) abd (5,t) What is the greatest ?

Question

In xy-coordinate plane, the graph of x=y^2 -4 intersects line A at (0,p) abd (5,t) What is the greatest possible value of the slope of line A?

Answer 1

At x = 0 there are two possible values of y: p = 2 or p = -2

At x = 5 there are two possible value of y: t = 3 or t = -3

You have a total  of 4 points. By inspection you can see that (0,-2) and (5,3) will give the greatest slope. The x values are 0 and 5 so the difference in x will be the same for all the slopes between these points. You then want the two points that have the biggest y difference.

slope = (3 - (-2))/(5 - 0) = 5/5 = 1

The greatest slope will be 1

Answer 2

when x = 0, y = ±2, so least value of p is -2. when x = 5, y = ±3, so greatest value of t is 3.  From lowest point to highest, slope is (3 - -2)/(5 - 0) = 5/5 = 1