Question

A proportional relationship is shown in the table below: what is the slope and what numbers do i graph. ty besties

Answer 1

Answer:

The slope of the line is $m = \frac{3}{5}$ and the equation of the line is $y = \frac{3}{5}\cdot x$.

Step-by-step explanation:

From table we understand that slope of the line is constant, that is, for each change of $x$ there is one and only change in $y$, 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:

$m = \frac{y_{f}-y_{o}}{x_{f}-x_{o}}$ (1)

Where:

$x_{o}, x_{f}$ - Initial and final x-coordinates of the line.

$y_{o}, y_{f}$ - Initial and final y-coordinates of the line.

If we know that $(x_{o}, y_{o}) = (0,0)$ and $(x_{f},y_{f}) = (8,4.8)$, then the slope of the line is:

$m = \frac{4.8-0}{8-0}$

$m = \frac{3}{5}$

From graph we conclude that x-intercept of the line is $b = 0$. Hence, the equation of the line is $y = \frac{3}{5}\cdot x$ and we proceed to plot the expression with the help of a graphing tool.