Question

The following table shows the distance from school as a function of time:

Answer 1

Answer

(27,0); the distance away from the school

Answer 2

Answer: last option.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

$y=mx+b$

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

Find the slope of the line with this formula:

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

Choose two points from the table and substitute the coordinates into the formula. Then, the slope is:

$m=\frac{32-36}{3-0}=-\frac{4}{3}$

 By definition, the line intersects the y-axis when the value of "x" is zero.  So, based on the table, the y-intercept is:

$b=36$

Then the equation of the line is:

$y=-\frac{4}{3}x+36$

The line intersects the x-axis when the value of "y" is zero, then  substituting $y=0$ into the equation of this line, and solving for "x", you get:

$0=-\frac{4}{3}x+36\\\\(-36)(-\frac{3}{4})=x\\\\x=27$

So, the point of intersection with the x-axis is:

$(27,0)$

Since the table shows the distance from school as a function of time, you can conclude that meaning of the x-intercept in this scenario is: "The distance away from the school".