Can someone please help me understand linear equations?

I really have a hard time solving linear equations. My teacher is gone for a whole week for a golf tournament (he’s a golf coach) so I can't go to tutoring. I don't know who else to go to, so anyone who helps me understand how to do these questions, it is much appreciated. Thank you.





Problem:


H.E. Lansburg's Weather and Health reports data gathered during World War II which shows that people use about 30 more calories per day for each 1 degree drop in the Celsius temperature. AT 21 degrees C, a working person uses about 3000 calories per day.


a) Explain how you know that the calorie consumption varies linearly with the temperature. What is the slope? Write the particular equation.


b) How many calories per day would a working person use in:


-the Sahara desert, when the temperature is 50 degrees C?


-Antarctica in August, when the temperature is -50 degrees C?


c) At what temperature does your model predict that a working person would use no calories at all?

Can someone please help me understand linear equations?
So.... when degrees = 21, calories = 3000


It says that when the temp drops 1 degree, the calories increase by 30.


So... if degrees = 20, calories = 3030





Degrees would be your x value


Calories would be your y value





So, you have two points (21, 3000) and (20, 3030).





a) you know if varies linearly because each variable changes at a constant rate. (If you drop Degrees by 1 degree, Calories increases by 30. Therefore if you drop degrees by 10, calories increases by 300.)





Since you have two points (the two I gave above), you can write an equation.





Slope = (3030 - 3000) / (20 - 21) = 30 / (-1) = -30





Using point-slope form:


y - 3000 = (-30)(x - 21)


y - 3000 = -30x + 630


y = -30x + 3630





b)


Remember temperature is X, Calories is Y.


So...


Sahara = 50 Degrees


so, x = 50


Plug that into the equation from part a.


y = -30(50) + 3630


y = -1500 + 3630 = 2130





Antartica = -50 degrees


so, x = -50


You can work this one out to find y. (Just like the Sahara example I did.)





c)


If you want to use NO CALORIES, that means y = 0


so...


0 = -30x + 3630


solve for x.
Reply:a) as we know that for each drop of 1 degree we use up 30 calories more, we can say it's a linear variation as the drop is constant/uniform. i.e. for every drop of 1 degree, we use up 30 calories more. Its always the same.


a linear equation is given by the formula y = mx + c. y and x are variables that you wll plot on a graph. m (the gradient) and c (the intercept) can be calculated.


M is [change in y value] / [change in x value[. If we take degrees as x and calories as y, for every 1 degree drop we use up 30 calories more:


so: change in y will be +30 calories, and change in x would be -1 degree.


So m (gradient) would be +30/-1


which is = -30


So the slope will be negative sloping downwards from left to right.





C is the intercept, i.e. the point at which the line cuts the y axis (i.e. where x = 0)


we know that m = - 30.


we also know that at 21 degrees, a person uses 3000 calories. So at this temperature, x =21, y=3000


subsituting in our y=mx+c equation:


3000 = (- 30 * 21) + c


therefore c = 3000 + (30 *21)


c= 3630





So the equation for this linear relationship would be/;


y = - 30x + 3630


where y refers to calories and x to temperature.





Just substitute values into this equation to answer the rest of the questions.


(for (b) substitute 50 %26amp; -50 respectively for the x value


for (c) substitute '0' for y value)

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