Answer
[tex]-6x+y=43[/tex]
Explanation
The first thing we need to do is find the slope of our line. To do it we are using the slope formula:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
where
[tex]m[/tex] is the slope of the line
[tex](x_{1},y_{1})[/tex] are the coordinates of the first point on the line
[tex](x_{2},y_{2})[/tex] are the coordinates of the second point
From our graph we can get the points (0, 43) and (2, 55), so [tex]x_{1}=0[/tex], [tex]y_{1}=43[/tex], [tex]x_{2}=2[/tex], and [tex]y_{2}=55[/tex]. Let's replace the values in our slope formula:
[tex]m=\frac{55-43}{2}[/tex]
[tex]m=\frac{12}{2}[/tex]
[tex]m=6[/tex]
Now that we have our slope, we can use the point-slope formula:
[tex]y-y_{1}=m(x-x_{1})[/tex]
[tex]y-43=6(x-0)[/tex]
[tex]y-43=6x[/tex]
But remember that the equation of a line in standard form is [tex]Ax+Ay=C[/tex], so we need to subtract [tex]6x[/tex] and add 43 to both sides of our point slope equation:
[tex]y-43=6x[/tex]
[tex]-6x+y-43+43=6x-6x+43[/tex]
[tex]-6x+y=43[/tex]
We can conclude that the equation in standard form that represent the relationship in the graph is [tex]-6x+y=43[/tex].
