BPick two points that lie the line from Part A. Then, substitute their coordinates into the slope formula.
CSubstitute 350 for the variable that represents the number of Calories in the equation from Part B
AScatter Plot:
Example Line of Best Fit:
BExample Equation: y=10x+240 Interpretation of the Slope and Y-intercept: See solution.
CExample Conjecture: In a sandwich with 350 Calories there are about 11 grams of fat
Practice makes perfect
We are given a table that shows fat and Calories for fast food sandwiches.
Fat (grams)
21
10
14
21
30
34
32
37
27
26
18
7
Cost ($)
490
280
330
430
530
590
540
590
550
470
450
340
We are asked to construct a scatter plot and draw a line that best represents the data, which is a line of best fit. To construct a scatter plot, we need to sketch each point from the table. For example, let's sketch the first point from the table ( 21, 490) on a coordinate plane. The horizontal axis will represent fat amounts in grams and the vertical axis will represent numbers of Calories.
In a similar way, we will now graph the other points from the table.
We constructed a scatter plot of the data! Now let's draw a straight line that best represents the data. Remember that we should try for the line to be as close to the data points as possible.
Note that this is only an example of a line of best fit. Notice that, if you sketch a different line that is close to the data points, it would also be a correct answer.
In Part A, we chose the following line of fit.
Let's write an equation in slope-intercept form for this line!
y=mx+bIn this equation, m is the slope and b is the y-intercept. To find the slope m, we will choose any two points on the line.
The first point has coordinates x_1= 16 and y_1= 400. The second point has coordinates x_2= 26 and y_2= 500. Let's substitute these values into slope formula.
We found that the slope m is equal to 10. This means that as the number of grams of fat in a sandwich increase by 1, the number of Calories in the sandwich increase by 10.
y=mx+b ⇔ y= 10x+b
To find the y-intercept b, we can substitute any point from the line of fit into this equation and then solve for b.
We can see that the line of fit passes through the point with coordinates x= 16 and y= 400. Let's substitute them into the slope-intercept equation!
The y-intercept b is equal to 240. The y-intercept is the y-value — or in this case the number of Calories — when the x-value (fat) is equal to 0. Therefore, we can say that a sandwich with no grams of fat has about 240 Calories.
y=10x+b ⇕ y=10x+ 240
We wrote an equation of the line in slope-intercept form!
In Part B, we wrote an equation which approximates the number of Calories y in a sandwich with x grams of fat.
y=10x+240
We are asked to use this equation to make a conjecture about the number of grams of fat in a sandwich with 350 Calories. To do that, we need to substitute y=350 into our equation.
