Superman needs to save Lois from the clutches of Lex Luthor. After flying for 16 seconds, he is 1236 meters from her. Then at 19 seconds he is 1074 meters from her. Superman flies at a constant rate.

Question

What is Superman’s average rate? Meters per second

How far does Superman fly every 7 seconds? Meters

How close to Lois is Superman after 26 seconds? Meters

Answer 1

1. So average rate of change is the same as the slope. If you treat the data as points (16,1236) and (19,1074) and use the slope formula

=slope

=coordinates of first point in the line

=coordinates of second point in the line

Once you plug in the correct values you should get a rate of change or slope of -54

Now to solve part two and three we need to finish our formula. The formula I am referring to is the slope intercept formula y=mx+b

M-slope

B-y intercept or when x is zero what is our y value

x and y represent coordinate points

To find our b value we are going to plug in the values we know and solve for b

Using y=mx+b we are going to pick one of the points (16,1236). x=16, y=1236, and m=-54

1236=-54(16)+b

Once solved correctly you will get 2100 for b

So our formula is y=-54x+2100, now we can use that formula to solve the other questions

2.How far does superman fly after 7 seconds? Seconds are x values so plug 7 into the formula and solve for y

y=-54(7)+2100

So 1722 meters

3.How close is Lois after 26 seconds

y=-54(26)+2100

So 696 meters