Blood, Sweat, and tears

The objective of Day 2 is to learn how to write the linear of a line using the data from the line of best fit. The definition of line of best fit is, the curve of a line fitting is the process of constructing a curve, or mathematical function, that has the best fit to the series of points given.

The photograph that has been given above is the showing how the line is fitting to the best series of points that are given on the scatter plot.

The equation of a line is written in y=mx+b form where m is the slope and b is the y-intercept Example:

Find the equation of the line

Choose two points that are on the line

Find the slope in between the two points

$\\ m=\frac{y_{2}\, -y_{1}}{x_{2}\, -x_{1}}=\frac{\left (-1 \right )-3}{3-\left ( -3 \right )}=\frac{-4}{6}=\frac{-2}{3} \\$

We can find the b-value, the y-intercept, by finding it in the linear equation

b = 1

We've got a value for m and a value for b. This gives us the linear function

$\\ y=-\frac{2}{3}x+1 \\$

In many events the value of b is not as easily read. In those events, or if you're not sure whether the line actually goes across the y-axis in this point you can calculate b by figuring out the equation for b and than putting in x and y with one of your two points.

We can use the example above to illustrate this. We've got the two points (-3, 3) and (3, -1). From these two points we calculated the slope

$\\ m=-\frac{2}{3} \\$

This gives us the problem

$\\ y=-\frac{2}{3}x+b \\$

From this we can solve the problem for b

$\\ b=y+\frac{2}{3}x \\$

And if we put in the values from our first point (-3, 3) we get

$\\ b=3+\frac{2}{3}\cdot \left ( -3 \right )=3+\left ( -2 \right )=1 \\$

If we put in this value for b in the equation we get

$\\ y=-\frac{2}{3}x+1 \\$

which is the same equation as we got when we read the y-intercept from the graph.

To put it all together, how to write a linear equation using the slope-interception form you

1. Identify the slope, m. This can be done by calculating the slope between two points of the line using the slope formula.
2. Find the y-intercept. This can be done by putting the slope and the coordinates of a point (x, y) on the line in the slope-intercept formula and then solve for b.

Once you've got both m and b you can just put them in the equation at their natural position.

Quiz

1. (3,4) and (0,9)

2.(3,2)

3.(3,2) (-1,6)

Answer Key

2. y=2x-10

3. y=-x+5

Blood, Sweat, and tears

Thursday, May 16, 2013

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