Question

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

time in minutes. distance in meters
x. f(x)
0 36
3 32
6 28
9 24
12 20

find and intercept the meaning of the x intercept in this scenario
36,0 the distance away from the school
27,0 the time it takes to reach the school
36,0 the time it takes to reach the school
27,0 the distance away from the school​

Answer 1

A: 36,0 the distance away from the school

Explanation:

At 0 it means you have spent 0 minutes going to school which means you haven't left the starting point yet.

36 is the distance left (in meters) from your current position and school. This means that the school is 36 meters away from the starting point.

Answer 2

27,0 the distance away from the school​

Explanation:

Apply the formula for equation of a straight line;

y=mx+c where c is the y intercept , and m is the gradient

From the graph, the slope is negative where speed decreases with increase in time

Find the gradient by applying the formula;

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

Taking y₁=24, y₂=20, x₁=9, x₂=12

Then;

`m=(20-24)/(12-9) =(-4)/(3)`

write the equation of the function as ;

y=mx+c, c=36( the y-intercept when x=0) hence the equation is;

`y=mx+c\\\\y=(-4)/(3)x+36`

To get x-intercept, substitute value of y with 0

`y=mx+c\\\\\\y=-(4)/(3) +36\\\\\\0=-(4)/(3) x+36\\\\(4)/(3)x =36\\\\\\4x=36*3\\\\\\x=108/4=27`

This means that the x-intercept is 27 ,and this means you will require 27 minutes to cover the whole distance to the school.