Use the graph to answer the question.

image shows y axis 15 down to 0 and x axis -10 to 10. points -1, 10 and 1, 3.6 are shown

Which equation is shown in the graph? (1 point) Responses y=6⋅(3.6)x y is equal to 6 times 3 point 6 to the x th power y=6⋅0.6x y is equal to 6 times 0 point 6 x y=6⋅(0.6)x y is equal to 6 times 0 point 6 to the x th power y=10⋅(1.05)x

1 answer

To determine which equation corresponds to the points shown on the graph, we can analyze the provided points (-1, 10) and (1, 3.6).

First, let's check them against the proposed equations.

  1. For y=6(3.6)x:
    • When x=1: y=6(3.6)1=6/3.61.67 (not a match for y=10)
    • When x=1: y=6(3.6)1=21.6 (not a match for y=3.6)

This equation does not fit.

  1. For y=6(0.6)x:
    • When x=1: y=6(0.6)1=6/0.6=10 (matches!)
    • When x=1: y=6(0.6)1=60.6=3.6 (matches!)

This equation fits both points.

  1. For y=10(1.05)x:
    • When x=1: y=10(1.05)19.52 (not a match for y=10)
    • When x=1: y=10(1.05)1=10.5 (not a match for y=3.6)

This equation does not fit.

  1. For y=60.6x is essentially the same as the third equation expressed differently, so it will yield the same results as the previously evaluated y=6(0.6)x, confirming the match for both points as well.

Based on this analysis, the appropriate equation shown in the graph is y=6(0.6)x (which can also be referred to as y=60.6x).