Question

Which of the followingis equivalent to20 (4x + 3 8x) for allvalues of x

Answer 1

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:

`Ax+By=C`

When x=0, y=8, so the point is (0,8). We replace x and y and get:

`\begin{gathered} A\cdot0+B\cdot8=C \\ B=(C)/(8) \end{gathered}`

For the x-intercept we have the point (6,0), so replacing in the equation we get:

`\begin{gathered} A\cdot6+B\cdot0=C \\ A=(C)/(6) \end{gathered}`

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:

`\begin{gathered} C=24 \\ B=(C)/(8)=(24)/(8)=3 \\ A=(C)/(6)=(24)/(6)=4 \end{gathered}`

Then the equation can be written as:

`4x+3y=24`

Answer: 3y+4x=24