Question

Imagine a scatter plot was created based on the data in the table(I’ll send the image) which equation best represents the trend line for the data

Answer 1

y=(3/5)x+1

Step-by-step explanation:

We pick two points: (5,4) and (15,10) from the table.

Using the two-point form of the equation of a line:

`\begin{gathered} (y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1) \\ (y-4)/(x-5)=(10-4)/(15-5) \\ (y-4)/(x-5)=(6)/(10) \\ (y-4)/(x-5)=(3)/(5) \end{gathered}`

From the right side of the result above, the line has a positive slope, 3/5.

Next, when x=0

`\begin{gathered} y-4=(3)/(5)(x-5) \\ y-4=(3)/(5)(0-5) \\ y-4=(3)/(5)(-5) \\ y-4=-3 \\ y=4-3=1 \\ \text{The y-intercept, b=1} \end{gathered}`

Therefore, the equation that best represents the trend line is:

`y=(3)/(5)x+1`

The five points are plotted in the graph below for illustration with the slope and y-intercept highlighted: