We have a scatter plot.
The points in the scatterplot can be fitted with a linear regression model that will capture the relation between x and y with a linear equation.
We can draw this approximately as:
This line has a y-intercept at y=8 and an x-intercept at x=6, so we can write the equation in standard form and find the coefficients:
[tex]Ax+By=C[/tex]When x=0, y=8, so the point is (0,8). We replace x and y and get:
[tex]\begin{gathered} A\cdot0+B\cdot8=C \\ B=\frac{C}{8} \end{gathered}[/tex]For the x-intercept we have the point (6,0), so replacing in the equation we get:
[tex]\begin{gathered} A\cdot6+B\cdot0=C \\ A=\frac{C}{6} \end{gathered}[/tex]We then define a value for C so as to calculate A and B in function of C. The value for C is usually the minimum common multiple of 6 and 8, so it is 24. Then A and B are:
[tex]\begin{gathered} C=24 \\ B=\frac{C}{8}=\frac{24}{8}=3 \\ A=\frac{C}{6}=\frac{24}{6}=4 \end{gathered}[/tex]Then the equation can be written as:
[tex]4x+3y=24[/tex]Answer: 3y+4x=24
