MATH 2121 Lecture 1: Math 2121 - August 23rd - Straight Lines

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Published on 30 Sep 2016
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Math 2121 – Lecture 1 – 8/23
Introduction
Two types of Calculus:
The first is Integral Calculus – Finding areas, volumes etc. of geometric shapes
Area Fourmulas
oTriangle – ½ Base * Height
oSquare – Side^2
oRectangle – Length * Width
oCircle – Pi * radius^2
The first person to find the area, and volumes, of curved shapes was Archimedes about 2000 years ago
The second is differential Calculus – Finding rates of change, slopes of curves, speed, acceleration,
motion
The slope of a straight line:
m = (y2-y1)/(x2-x1) Where m = slope and (X1, Y1) and (X2,Y2)are coordinate pairs.
This formula DOES NOT WORK for curved graphs such as Y=X2. To find that slope we need to use
calculus.
In this class we will focus primarily on Differential Calculus and in 2122 we will work with Integral
Calculus. We will start calculus after a few classes of algebra review.
Review of Straight Lines
For straight lines the most important thing to know is the slope of the line. Which, again, is:
m = (y2-y1)/(x2-x1) Where m = slope and (X1, Y1) and (X2,Y2)are coordinate pairs. (also m=rise/run)
Vertical Lines (lines that go straight up and down on the graph) do not have slopes.
oThese lines are not graphs of functions.
We can rewrite the equation of slope to the slope Intercept form by multiplying both sides by
(X2-X1) This would give us:
m(x2-x1) = (y2-y1) which can also be written as: y-y1 = m(x-x1)
Example 1:
Given the point (2,3) and a slope of 5, we can find the slope intercept form.
Y - y1 = m ( x – x1 )
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We simply insert our given quantities into the formula.
Y – 3 = 5 ( x – 2 )
Using this we can find the Y intercept form. Which is the Y = Slope*X – Y intercept. All we have to do is
solve for y
y – 3 = 5x - 10
y = 5x - 7
Example 2:
Given the Points (1,2) and (5,1) find the Y intercept form.
For this problem we are going to need to first find the slope.
m = ( 1 – 2 ) / ( 5 – 1 )
m = -1/4
So the slope of this line is going to be -1/4
Now using our slope and EITHER point, we can find the slope intercept (I’m going to do both just to
prove that it doesn’t matter which we choose)
Point (1,2)
Y - y1 = m ( x - x1 )
Y – 2 = ( -1/4 ) ( x – 1 )
I don’t like using fractions so we’re going to multiply both sides by 4 for now to get rid of it.
4 ( y – 2 ) = 4 ( (-1/4) ( x – 1 ) )
4y – 8 = - ( x – 1 )
4 y – 8 = -x + 1
4y = -x + 9
Y = (-1/4)x + (9/4)
Point (5,1)
Y – 1 = ( -1/4 ) ( x – 5 )
4 ( y – 1 ) = 4 ( (-1/4) ( x – 5 ) )
4y – 4 = - ( x – 5 )
4y – 4 = -x + 5
4y = -x + 9
find more resources at oneclass.com
find more resources at oneclass.com
Y = (-1/4)x + (9/4)
find more resources at oneclass.com
find more resources at oneclass.com