Question

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After 30 baseball games, Bryce Harper had 25 hits and after 100 games he had 165 hits. How many hits would he have after 106 games?(include units)
Find Slope(Rate of Change):
Then Find the Amount After 106 games.

Answer 1

Take 2 points

• (30,25)
• (100,165)

Slope:-

`\\ \rm\hookrightarrow m=(165-25)/(100-30)`

`\\ \rm\hookrightarrow m=(140)/(70)=2`

Equation in point slope form

`\\ \rm\hookrightarrow y-25=2(x-30)`

`\\ \rm\hookrightarrow y-25=2x-60`

`\\ \rm\hookrightarrow 2x-y-35=0`

• Convert to slope intercept form y=mx+b

`\\ \rm\hookrightarrow y=2x-35`

• Put x=106

`\\ \rm\hookrightarrow y=2(106)-35=212-35=177`

Answer 2

177 hits

Explanation:

Let
`x` = number of baseball games

Let
`y` = number of hits

(30, 25) =
`(x_1,y_1)`

(100, 165) =
`(x_2,y_2)`

Slope formula:
`m=(y_2-y_1)/(x_2-x_1) =(165-25)/(100-30) =2`

Using the point-slope formula to create an equation:

`y-y_1=m(x-x_1)\\\\\implies y-25=2(x-30)\\\\\implies y=2x-35`

Now substitute
`x = 106` into the equation and solve for
`y`:

`\implies y=(2 * 106)-35=177`

Therefore, the number of hits Bryce would have after 106 games is 177