08-27-2016, 04:08 AM

been awhile since I've done this so I may be doing it wrong, but this is what I think

the equation of a line is

y = mx + b

where m is the slope and b is the y intercept

on the graph x is the hours and y is the miles

why ?

because the speed is

miles

-----

hour

and slope is

change in y

-----------

change in x

so miles must be y and hour must be x

the equation for car A is

y = mx + b

y = 50x + 1

we use 1 for the y intercept because car A has a one mile headstart

so its starting point is not at the origin, but one mile ahead

the equation for car B is

y = 51x + 0

or

y = 51x

we use 0 for the y intercept because car B is starting at point zero

so if y = 51x in the 2nd equation, then substitute 51x for y in the first equation

51x = 50x + 1

subtract 50x from both sides

1x = 1

divide both sides by 1

x = 1

x is one so in one hour B catches up with A

now watch somebody smart come along and show how this is completely wrong

the equation of a line is

y = mx + b

where m is the slope and b is the y intercept

on the graph x is the hours and y is the miles

why ?

because the speed is

miles

-----

hour

and slope is

change in y

-----------

change in x

so miles must be y and hour must be x

the equation for car A is

y = mx + b

y = 50x + 1

we use 1 for the y intercept because car A has a one mile headstart

so its starting point is not at the origin, but one mile ahead

the equation for car B is

y = 51x + 0

or

y = 51x

we use 0 for the y intercept because car B is starting at point zero

so if y = 51x in the 2nd equation, then substitute 51x for y in the first equation

51x = 50x + 1

subtract 50x from both sides

1x = 1

divide both sides by 1

x = 1

x is one so in one hour B catches up with A

now watch somebody smart come along and show how this is completely wrong