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The first example here is just basic, given slope and a point, write the equation of the
line. We are going to use our point-slope form y minus y1 equals m times x minus x1.
I've got my slope that I can put in form and my point x1 y1 so y minus 4 is equal to negative
3 times x minus negative 2. y minus 4 is equal to negative 3 times x plus 2. Y minus 4 is
equal to negative three x minus 6 (all I did was distribute the negative 3). And then add
four to both sides to solve for y. y equals negative 3x minus 2. So that is just a basic
example of writing an equation of a line. Here we have the underground temperature.
So this one is a little more - it is a word problem. And this is 90 degrees Celsius and
370 degrees Celsius. We are supposed to write an equation to describe the relationship.
First you have to pick the independent variable and dependent variable. Now, little hint - because
it says that temperature varies with depth, it kind of gives it away for you that temperature
is your dependent variable and depth is your independent variable. So very easily you can
get two ordered pairs. 2km with 90 degrees Celsius and 10km with 370 degrees Celsius.
We need to find the slope. This is just the change in y divided by the change in x. So
it's the change in our dependent variable divided by the change in our independent variable.
So substitute in 370 minus 90 and 10 minus 2. 280 divided by 8 and so we have a slope
of 35 degrees Celsius per km. So that is our temperature change per kilometer. Now that
we have our slope, all you need is slope and a point. So pick whatever point you want.
I am going to pick this first one here and we are going to use our point-slope form just
like we did in the last example. y minus y1 which is y minus 90 equals our slope, 35 times
x minus the x coordinate. y minus 90, I am going to distribute here, equals 35x minus
70. Add 90 to both sides to solve for y and so here is my equation y equals 35x... y equals
35x minus 20. So remember that 35 is our temperature change per km of depth and this minus 20 for
us means that if we had 0 depth (we were at sea level) the temperature in degrees Celsius
would be negative 20. We can use the equation from the previous slide to do a couple of
predictions which are just basic plugging in. So our equation was y = 35x - 20. Use
the equation to predict the temperature at a depth of 13km. So temperature was y. So
y = 35 times 13 minus 20. This is just basic algebra here. You should have gotten 435 degrees
Celsius. And the second part. Use the equation to predict the depth if the temperature is
500 degrees Celsius. So 500 equals 35x - 20. Now we will solve for our other variable.
So 520 equals 35x. We are going to divide both sides by 35 and it looks like we get
something around 14.86km. Units are important.