Answer:
y=(3/5)x+1
Explanation:
We pick two points: (5,4) and (15,10) from the table.
Using the two-point form of the equation of a line:
[tex]\begin{gathered} \frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1} \\ \frac{y-4}{x-5}=\frac{10-4}{15-5} \\ \frac{y-4}{x-5}=\frac{6}{10} \\ \frac{y-4}{x-5}=\frac{3}{5} \end{gathered}[/tex]
From the right side of the result above, the line has a positive slope, 3/5.
Next, when x=0
[tex]\begin{gathered} y-4=\frac{3}{5}(x-5) \\ y-4=\frac{3}{5}(0-5) \\ y-4=\frac{3}{5}(-5) \\ y-4=-3 \\ y=4-3=1 \\ \text{The y-intercept, b=1} \end{gathered}[/tex]
Therefore, the equation that best represents the trend line is:
[tex]y=\frac{3}{5}x+1[/tex]
The five points are plotted in the graph below for illustration with the slope and y-intercept highlighted:
