~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.

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Presentation transcript:

~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 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.

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

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.

 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.

Can the temperature 0–7 hours after sunrise be represented by a linear function? If yes, find the equation of the function.

Temperature (°F) Hours after sunrise

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

Temperature (°F) Hours after sunrise

 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

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

 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.

~ms. dambreville