Similar triangles ABE and BCD are shown on the coordinate plane. Line t passes through points A, B and C.

The slope of segment AB is equal to the slope of segment BC.

Part A- Use the ratios of the side lengths of triangle ABE and triangle BCD to explain your answer.

Part B- write an equation for line t. Show or explain how you determined your equation.

A, B, C, E

Step-by-step explanation:

It can be seen from the figure that the points A, B, C and D, all are lying in the line t.

=> So that it can be concluded that AC and BC and BD have the slopes which are equal to each other and also equal to the slop of line t

So that all answer A, B, C are true.

In addition, as FD is parallel with x - axis, so that slope of the line t is equal to tan angel FDB

As FDB is the right triangle with BFD = 90°

=> tan angel FDB = FB/ FD (tan of an acute angel in the right triangle = opposite side/ adjacent side)

=> Slope of the line t is equal to FB/ FD

=> Answer E is true