After 22 games, JD Drew had 32 hits. After 36 games he had 60 hits.

Question

Write a linear equation in slope-intercept form to describe the situation.

Answer 1

To write a linear equation in slope-intercept form describing the situation, we need to find the slope of the line connecting the two points given by the games played and the corresponding number of hits. The slope-intercept form of a line is given by:

y = mx + b

where y is the dependent variable (number of hits), x is the independent variable (number of games), m is the slope of the line, and b is the y-intercept (the value of y when x is 0).

First, we determine the slope (m) using the given points:

Point 1: (x1, y1) = (22 games, 32 hits)
Point 2: (x2, y2) = (36 games, 60 hits)

The formula for the slope (m) is:

m = (y2 - y1) / (x2 - x1)

Plugging in the values:

m = (60 hits - 32 hits) / (36 games - 22 games)
m = 28 hits / 14 games
m = 2 hits per game

This means that JD Drew is getting 2 hits per game.

Now, we need to find the y-intercept (b). We can use one of the points and the slope to solve for b:

Taking point 1 for example:

y1 = m * x1 + b
32 hits = (2 hits/game) * (22 games) + b

Now we solve for b:

32 hits = 44 hits + b
b = 32 hits - 44 hits
b = -12 hits

So the y-intercept is -12.

Now we can write the linear equation in slope-intercept form:

y = 2x - 12

Thus, this equation models the relationship between the number of games JD Drew played and the number of hits he has in this particular time span.