He rate of change of a car is decreasing linearly by 10 miles per hour. before the car started to slow down, the car was traveling at 50 miles per hour. can you use a linear model to represent the cars speed as a function of time and if so, why? what is the value for the slope and the y-intercept?

Yes. It should be y= – 10x+50
This is in standard form, and it means that for every hour (x) you decrease by 10, starting point being 50. Y=50-10x wouldn’t be in standard form so I just moved it around.
You can use a linear model to represent the car’s speed as a function of time because the speed linearly decreases over time at an initial speed of 50mph, so y=–10x+50.
The value for the slope is –10, because the car’s speed is decreasing linearly.
The y intercept can be found when you substitute 0 for x.
-10(0) +50
Y intercept = 50
This means that at 0 hours, the cars speed is 50 mph.
Whoops this is too long but I don’t want have to write it over so good luck.