SOLUTION: Scenario: Advertiser's of a new refrigeration process claimed that the temp of a freezer, which starts at -2 degrees Celsius, can be reduced by 1 degree per minute. To write an

Question 571302: Scenario: Advertiser's of a new refrigeration process claimed that the temp of a freezer, which starts at -2 degrees Celsius, can be reduced by 1 degree per minute.
To write an expression, define a variable for the time in minutes use this variable to write a rule for the temperature.
I already have a predone graph that goes from 5 to -5 degrees on the vertical and on horizontal it goes from -5 to 5 in time. There is also a predetermined diagonal line on the graph that spans from 3 degrees celsius on the horizon to 3 degrees on the time line and on this line it has a dot at intersecting point -2 celsius and 0 on the minutes, it also has one below that on -3 degrees and 1 on minutes.
At the bottom of the graph the question asks to enter the y intercept of the line and then asks to enter the slope of the line. I'm failing 9th grade algebra and I dont quite understand the question so any help would be greatly appreciated and if you could explain how its done to where I could possibly understand it would be even better. Thank you in advance.
Answer by KMST(893) (Show Source):
You can put this solution on YOUR website!
I would say:
"Let x be the time in minutes."
That is defining a variable for the time in minutes. That would be considered your independent variable.
You could also say "Let y be the temperature in degrees Celsius," to define your dependent variable.
Your graph must look like this
and represents the variation of the temperature with time.
It's supposed to help you answer the question.
The upper dot represent the point where the timer is started, and the starting temperature is measured as -2 degrees Celsius.
The lower dot represents the point, one minute later, when the temperature is measured again and we see that it's -3 degrees Celsius.
The temperature was reduced by one degree in one minute as advertised.
From the graph you can also see what the temperature would be at 3,4, an 5 minutes. You can even see what the temperature must have been 5 minutes before the start, at x=-5 minutes, where the line tells you that the temperature was y=3 degrees Celsius.
The "rule for the temperature" that the problem asks for is .
You can see that describes that line, because for any point on that line, if you plug into that formula the time (x) for the point, the formula gives you the temperature (y).
For example, at the start, represented by the upper dot, x=0, and the formula for the line calculates

For the lower dot, x=1, and the formula says .
For the point at the right end of the graph, x=3, and y=-3-2=-5.
The slope of a line is defined as the change as the independent variable increases by 1. The independent variable is usually called x, and that is what my graph says, but you could call it t.
The slope of your line is -1, because as x increases by 1, the change to y (the temperature) is -1.
The y-intercept is the y value for the point where the line crosses the y-axis. In this case the y-intercept is -2.
In general, the slope can be calculated from the coordinates of two points as difference in the y values divided by the corresponding difference in the x values. The coordinates for the two points marked by dots/circles on the graph are:
for the upper dot: (0,-2) or x=0, y=-2
for the lower dot: (1,-3) or x=1, y=-3
The slope would be calculated as