Question

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

Time (in minutes)
x Distance (in meters)
f(x)
0 45
3 40
6 35
9 30
12 25


Find and interpret the meaning of the x-intercept in this scenario.
(45, 0); the distance away from the bus stop
(27, 0); the time it takes to reach the bus stop
(45, 0); the time it takes to reach the bus stop
(27, 0); the distance away from the bus stop

Answer 1

Answer: (27, 0); the distance away from the bus stop

Answer 2

Answer: LAST OPTION.

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=(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=(40-45)/(3-0)=-(5)/(3)`

By definition, the line intersects the y-axis when the value of "x" is zero (
`x=0`).

Based on the table, the y-intercept is:

`b=45`

Then the equation of the line is:

`y=-(5)/(3)x+45`

The line intersects the x-axis when the value of "y" is zero (
`y=0`), then you can substitute these value into the equation and solve for "x":

`0=-(5)/(3)x+45\\\\x=27`

So, you get the point:

`(27,0)`

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