~adapted from Walch Education A scatter plot that can be estimated with a linear function will look...
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FITTING LINEAR FUNCTIONS TO DATA ~adapted from Walch Education
~adapted from Walch Education A scatter plot that can be estimated with a linear function will look approximately like a line. A line through two points
A scatter plot that can be estimated with a linear function
will look approximately like a line. A line through two points in
the scatter plot can be used to find a linear function that fits
the data. If a line is a good fit for a data set, some of the data
points will be above the line and some will be below the line.
Slide 4
The general equation of a line in point-slope form is y = mx +
b, where m is the slope and b is the y- intercept. To find the
equation of a line with two known points, calculate the slope and
y-intercept of a line through the two points. Slope is the change
in y divided by the change in x; a line through the points (x 1, y
1 ) and (x 2, y 2 ) has a slope of
Slide 5
To find the y-intercept, or b in the equation y = mx + b,
replace m with the calculated slope, and replace x and y with
values of x and y from a point on the line. Then solve the equation
for b. o For example, for a line with a slope of 2 containing the
point (1, 3), m = 2 3 = (2)(1) + b 5 = b.
Slide 6
A weather team records the weather each hour after sunrise one
morning in May. The hours after sunrise and the temperature in
degrees Fahrenheit are in the table to the right.
Slide 7
Can the temperature 07 hours after sunrise be represented by a
linear function? If yes, find the equation of the function.
Slide 8
Temperature (F) Hours after sunrise
Slide 9
1. Determine if the data can be represented by a linear
function. The temperatures appear to increase in a line, and a
linear equation could be used to represent the data set. 2. Draw a
line to estimate the data set. Two points in the data set can be
used to draw a line that estimates that data. A line through (2,
56) and (6, 64) looks like a good fit for the data
Slide 10
Temperature (F) Hours after sunrise
Slide 11
Find the slope, m, of the line through the two chosen points.
The slope is = For the two points (2, 56) and (6, 64), the slope
is
Slide 12
Finding the y-intercept, b: Use the general equation of a line
to solve for b. Substitute x and y from a known point on the line,
and replace m with the calculated slope. y = mx + b For the point
(2, 56): 56 = 2(2) + b b = 52
Slide 13
Replace m and b with the calculated values in the general
equation of a line. y = 2x + 52 The temperature between 0 and 7
hours after sunrise can be approximated with the equation y = 2x +
52.
