*Milestones review due Fri 3/23  Today Is… Thurs , March 22nd DO NOW: Get worksheet from table & get out homework Warm-up Announcements: *skills check Monday 3-26 (scatter plots & line of best fit) *U6 test Fri 3/30 *8th tshirt money due Wed, March 28th * Olympic tshirt money extended to March 30 HW *Milestones review due Fri 3/23 Today in class students will be learning…. Today I am learning systems of equations because they can be used to compare information in areas of money, profit, loans etc. as well as correlations in many areas. .

Lines of Best Fit When data show a correlation, you can estimate and draw a line of best fit that approximates a trend for a set of data and use it to make predictions. Line of Best Fit: a straight line that comes closest to the points on a scatter plot. Steps for Drawing the Line of Best Fit: 1.) Plot the data as ordered pairs – make a scatter plot. 2.) Study the points to see if there is a relationship between the 2 sets of data – positive, negative, or no association (see Data Relationships slide).

Data Relationships There are three ways to describe data displayed in a scatter plot and the adjectives “strong” and “weak” can also be used to further define the association. Positive Association Negative Association No Association The values in both data sets increase or decrease at the same time. The values in one data set increase as the values in the other set decrease. The values in both data sets show no pattern.

Steps for Drawing a Line of Best Fit (cont.): 3.) Draw a line of best fit. It should be as close as possible to most of the points – look for the center – and go in the same direction as the points. Try to draw the line so that about the same number of points are above the line as below the line. Draw the line so that it goes through some corners where the grid lines meet (integers) to help you write the equation of the line of best fit in slope-intercept form (y=mx+b).

Which graph shows the line of best fit? Why? D.

Writing an Equation for the Line of Best Fit Once you’ve drawn a line of best fit, you can find the slope, y-intercept, and write the equation of the line – just like with any linear function. Slope: Pick 2 points on the line where it meets the corners where the x & y grid lines intersect (to get integers). Then use the slope formula/L method. Y-intercept: Use slope and one point (x,y) in the slope-intercept form (y=mx+b) and solve for b. To estimate b, look at where the line crosses the y-axis. Equation: Write in slope-intercept form: y = mx + b using the m and b values you calculated.

Example 1 – Data & Line of Best Fit

Example 2 – Data & Line of Best Fit

Example 3 – Data & Line of Best Fit Years since 1990 weight (lb) 100 120 140 160 180 2 4 6 8 10 200

Warm-up 3/21 Years since 1990 weight (lb) 100 120 140 160 180 2 4 6 8 10 200 Based off of the line of best fit, what is the initial value (y-int) in the following graph? Write an equation for the line of best fit.

Height Conversion Chart Height (ft) Height (in) 4’10’’ 58 5’6’’ 66 4’11’’ 59 5’7’’ 67 5’0’’ 60 5’8’’ 68 5’1’’ 61 5’9’’ 69 5’2’’ 62 5’10’’ 70 5’3’’ 63 5’11’’ 71 5’4’’ 64 6’0’’ 72 5’5’’ 65 6’1’’ 73

Warm-up 3/22 Based off of the line of best fit, what is the initial value in the following graph? Write linear model (equation) for the line of best fit.

After your Skills Check Turn into my inbox Complete Height vs. Shoe Size Task (due tomorrow). You may turn in now if you are finished! Complete Scatterplot review for Friday’s Quiz

Warm-up 3/23 For each problem, choose which equation has a greater rate of change? *Hint: think about which slope would be steeper a) 𝑦=3𝑥+5 b) 𝑦= 1 3 𝑥+7 a) 𝑦=−7𝑥−2 b) 𝑦=− 3 5 𝑥 3. a) 𝑦=3𝑥+5 b) 𝑦=−7𝑥−2

Warm-up 3/23 Order the equations from smallest rate of change to greatest rate of change. a) 𝑦=3𝑥+5 b) 𝑦= 1 3 𝑥+7 c) 𝑦=−7𝑥−2 d) 𝑦=− 3 5 𝑥

Warm-up 3/24 Which table shows the lowest rate of change (slope)? Which shows the greatest? a) b) c) x y 1 2 3 4 5 6 x y 1 3 2 -2 -7 x y 1 3 2 5

Warm-up 3/24 From the tables, determine if the rate of change is increasing or decreasing a) b) c) x y 1 2 3 4 5 6 x y 1 3 2 -2 -7 x y 1 3 2 5