Question

A table of values of a linear function is shown below

Answer 1

We are given a table of values of a line function.

The y-intercept of a line is the point where the line intercepts the y-axis. At this point, the value of "x" is zero.

From the table, we look in the row for the x-values the entry for zero. The associated value to that entry is the y-intercept, therefore, we have:

$y-intercept=7$

To determine the slope we will use the following formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

Where:

$\begin{gathered} (x_1,y_1);(x_2,y_2) \\ \end{gathered}$

are values in the table. We choose the first two values:

$\begin{gathered} (x_1,y_1)=(0,7) \\ (x_2,y_2)=(1,4) \end{gathered}$

Substituting the values we get:

$m=\frac{4-7}{1-0}$

Solving the operations:

$m=-3$

Therefore, the slope is -3

To determine the equation of the line we use the slope-intercept form of a line equation:

$y=mx+b$

Where "m" is the slope, and "b" is the y-intercept.

Substituting we get:

$y=-3x+7$

And thus we get the equation of the line.