Answer:
The slope of the line is [tex]m = \frac{3}{5}[/tex] and the equation of the line is [tex]y = \frac{3}{5}\cdot x[/tex].
Step-by-step explanation:
From table we understand that slope of the line is constant, that is, for each change of [tex]x[/tex] there is one and only change in [tex]y[/tex], fulfilling the main characteristic of a line and we can determine the slope for every point of the line by means of the following expression:
[tex]m = \frac{y_{f}-y_{o}}{x_{f}-x_{o}}[/tex] (1)
Where:
[tex]x_{o}, x_{f}[/tex] - Initial and final x-coordinates of the line.
[tex]y_{o}, y_{f}[/tex] - Initial and final y-coordinates of the line.
If we know that [tex](x_{o}, y_{o}) = (0,0)[/tex] and [tex](x_{f},y_{f}) = (8,4.8)[/tex], then the slope of the line is:
[tex]m = \frac{4.8-0}{8-0}[/tex]
[tex]m = \frac{3}{5}[/tex]
From graph we conclude that x-intercept of the line is [tex]b = 0[/tex]. Hence, the equation of the line is [tex]y = \frac{3}{5}\cdot x[/tex] and we proceed to plot the expression with the help of a graphing tool.
