Q:

What is the rate of change and initial value for the linear relation that includes the points shown in the table?x y1 203 105 07 βˆ’10

Accepted Solution

A:
Each time x increases by 2 (eg from x = 1 to x = 3), the value of y drops by 10 (eg from y = 20 to y = 10)

Therefore the slope is...
slope = rise/run = (change in y)/(change in x) = -10/2 = -5
slope = -5

So each time x increases by 1, y will decrease by 5
Flip things around: each time x decreases by 1, y will increase by 5

So the pair (x,y) = (1,20) shown in row 1 of the table leads to (0,25) based on the rule above. Another way to see this is to plug m = -5, x = 1 and y = 20 into y = mx+b and solve for b to get b = 25

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Answers:
Rate of change = -5
Initial value = 25

Notes: slope is another term for rate of change. The y intercept is another way of stating the initial value