Question

Sonja plays tennis and started a tournament with 43 aces on the season. The graph relates her total season aces with the number of matches played in the tournament.

Answer 1

-6x+y=43

Explanation:

I took the test and got it right

Answer 2

`-6x+y=43`

Explanation

The first thing we need to do is find the slope of our line. To do it we are using the slope formula:

`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

where

`m` is the slope of the line

`(x_(1),y_(1))` are the coordinates of the first point on the line

`(x_(2),y_(2))` are the coordinates of the second point

From our graph we can get the points (0, 43) and (2, 55), so
`x_(1)=0`,
`y_(1)=43`,
`x_(2)=2`, and
`y_(2)=55`. Let's replace the values in our slope formula:

`m=(55-43)/(2)`

`m=(12)/(2)`

`m=6`

Now that we have our slope, we can use the point-slope formula:

`y-y_(1)=m(x-x_(1))`

`y-43=6(x-0)`

`y-43=6x`

But remember that the equation of a line in standard form is
`Ax+Ay=C`, so we need to subtract
`6x` and add 43 to both sides of our point slope equation:

`y-43=6x`

`-6x+y-43+43=6x-6x+43`

`-6x+y=43`

We can conclude that the equation in standard form that represent the relationship in the graph is
`-6x+y=43`.