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

Answer

$-6x+y=43$

Explanation

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

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

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:

$m=\frac{55-43}{2}$

$m=\frac{12}{2}$

$m=6$

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 $-6x+y=43$.