~adapted from walch education a scatter plot that can be estimated with a linear function will look...
TRANSCRIPT
- Slide 1
- Slide 2
- ~adapted from Walch Education
- Slide 3
- 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.
- Slide 14
- ~ms. dambreville