Question

Use the graph below to answer the following question Which equation could describe the line of best fit for the graph above?A y=5x+236B y=-5x+236C y=1/5x+236D y=-1/5+236

Answer 1

Consider that the equation of a line with slope 'm' and y-intercept 'c', is given by,

`y=mx+c`

Also, the slope of a line making angle Θ with positive x-axis, is defined as,

`m=\tan \theta`

And we know that,

`\begin{gathered} m>1\Rightarrow\theta>45 \\ m<1\Rightarrow\theta<45 \end{gathered}`

Now, observe the data points. It is seen that 'y' is increasing with 'x', so the slope of the best fit line must be positive.

Therefore, options B and D are eliminated, since they have slopes -5 and -1/5respectively.

Again, from the graph it is observed that the data on the y-axis is quite large as compared to the data on x-axis.

So the best fit line must be inclined at a very large angle from the positive x-axis i.e. it should lie closer to the y-axis. Then the slope of the line must be greater than 1.

Therefore, option C is also eliminated since its slope is 1/5.

Thus, from the above discussion, it is concluded that option A is the correct choice.

However, you may verify that the equation y = 5x + 236