To write a linear equation in slope-intercept form (y = mx + b), we need to determine two things: the slope (m) and the y-intercept (b).
In this situation, let's say 'x' represents the number of games played, and 'y' represents the number of hits.
We are given two points corresponding to the (x, y) pairs: (22, 32) and (36, 60).
First, we calculate the slope (m), which is the change in hits divided by the change in games played. The formula for the slope (m) between two points (x1, y1) and (x2, y2) is:
m = (y2 - y1) / (x2 - x1)
For the given points, this becomes:
m = (60 - 32) / (36 - 22)
m = 28 / 14
m = 2
So the slope is 2, which means JD Drew gets 2 hits per game.
Now we use one of the points and the slope to find the y-intercept (b). We can use the slope-intercept formula and plug in the values for one point and m:
y = mx + b
Using the first point (22, 32):
32 = 2(22) + b
32 = 44 + b
b = 32 - 44
b = -12
Therefore, the y-intercept (b) is -12.
Now we have both the slope and the y-intercept, so we can write the linear equation:
y = 2x - 12
This equation tells us that for every game (x), JD Drew is expected to have 2x - 12 total hits (y) based on the trend from the first 36 games.
After 22 games, JD Drew had 32 hits. After 36 games he had 60 hits.
Write a linear equation in slope-intercept form to describe the situation.
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