Question

Let y=3t+6 be a linear function representing the distance from home for an ant t minutes after starting out from a location near its home. What does the number 6 represent in this function?

Answer 1

The format that this fits in is y=mx+b where m=slope and b=y intercept. So 6 is the y-intercept.

Hope this helps.

Answer 2

Here 6 represents the initial distance of the ant from the home.

( i.e. initially when t=0 the ant was at a distance of 6 units from the home )

Explanation:

The linear function which represents the distance from home for an ant t minutes after starting out from a location near its home is given by:

y=3t+6

We know that for any linear function of the type:

y=mx+c

m represents the slope and c represents the y-intercept of the function.

i.e. m represents the per unit change and c represent the initial value i.e. when t=0

Here we have: c=6

i.e. it represents the initial distance of the ant from the home.