MATHEMATICS MIDDLE SCHOOL

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

Answers

Answer 1

Answer:

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:

$m=(y_2-y_1)/(x_2-x_1)$

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":

$0=-(5)/(3)x+45\n\nx=27$

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".

Answer 2

Answer:

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

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