The distance traveled by both cars is an illustration of a linear function.
Car A
Speed = 45 miles per hour
So, the coordinates of car A are:
[tex]\mathbf{(x,y) = (8,0) (9, 45) (10, 90) ....}[/tex]
Car B
Speed = 60 miles per hour
So, the coordinates of car B are:
[tex]\mathbf{(x,y) = (9, 0) (10, 60) (11, 120) ....}[/tex]
(a) The equation of both cars
Car A
This is calculated as:
[tex]\mathbf{y = mx+ b}[/tex]
Where m represents slope/speed.
So, m = 45
This gives
[tex]\mathbf{y = 45x + b}[/tex]
y = 0, when x = 8.
So, we have:
[tex]\mathbf{0= 45\times 8 + b}[/tex]
[tex]\mathbf{0= 360 + b}[/tex]
Solve for b
[tex]\mathbf{b=- 360}[/tex]
So, the equation of car A is:
[tex]\mathbf{y=45x - 360}[/tex]
Car B
This is calculated as:
[tex]\mathbf{y = mx+ b}[/tex]
Where m represents slope/speed.
So, m = 60
This gives
[tex]\mathbf{y = 60x + b}[/tex]
y = 0, when x = 9.
So, we have:
[tex]\mathbf{0= 60\times 9 + b}[/tex]
[tex]\mathbf{0= 540 + b}[/tex]
Solve for b
[tex]\mathbf{b=- 540}[/tex]
So, the equation of car B is:
[tex]\mathbf{y=60x - 540}[/tex]
(b) The graphs
See attachment
(c) The time which both cars meet
We have:
[tex]\mathbf{y=60x - 540}[/tex] and [tex]\mathbf{y=45x - 360}[/tex]
Equate both
[tex]\mathbf{60x - 540=45x - 360}[/tex]
Collect like terms
[tex]\mathbf{60x - 45x = 540- 360}[/tex]
[tex]\mathbf{15x = 180}[/tex]
Divide both sides by 15
[tex]\mathbf{x = 12}[/tex]
This means that both cars meet at 12:00pm
Read more about linear functions at:
https://brainly.com/question/20286983
