Question

To find the solution to a system of linear equations, Verdita begins by creating equations for the two sets of data points below.

Data Set A
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 1, 1, 5, 7. Column 2 is labeled y with entries negative 6, 2, 18, 26.
Data Set B
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 5, negative 2, 0, 6. Column 2 is labeled y with entries negative 1, 2, 4, 10.

Which equations could Verdita use to represent the data sets?
Data Set A: y = 4 x minus 2
Data Set B: y = x + 4
Data Set A: y = 4 x minus 2
Data Set B: y = x minus 4
Data Set A: y = 4 x + 2
Data Set B: y = x minus 4
Data Set A: y = 4 x + 2
Data Set B: y = x + 4



Name Plates
A graph has letters on the x-axis and length (inches) on the y-axis. A trend line goes through points (2, 4) and (9, 16). The regression equation is y = 1.75 x + 0.5.


A customer would like the company to build him a name plate that is 22 inches long. What is the best estimate of the number of letters the company can have on the name plate?
9
10
12
39

Answer 1

The correct equations that represent Data Sets A and B are y = 4x - 2 and y = x + 4 respectively. For the name plate length problem, the best estimate for the number of letters that can fit on a 22-inch name plate is 12 letters. Therefore correct option is C.

Step-by-step explanation:

To determine which equations could represent Data Sets A and B, we need to analyze the given points to figure out the slope and y-intercept of the line that fits the data.

For Data Set A, let's look at two points from the table: (1, 2) and (5, 18). We can use these points to calculate the slope (m) as follows:

m = (y2 - y1) / (x2 - x1) = (18 - 2) / (5 - 1) = 16 / 4 = 4.

Now we use the slope and one of the points to find the y-intercept (b). Using (1, 2):

2 = 4(1) + b, which yields b = -2.

So, the equation for Data Set A is y = 4x - 2.

For Data Set B, using the points (-5, -1) and (0, 4), again we calculate the slope (m):

m = (4 - (-1)) / (0 - (-5)) = 5 / 5 = 1.

With the y-intercept given by the point (0, 4), the equation for Data Set B is y = x + 4.

Therefore, the correct pair of equations for the data sets is:

• Data Set A: y = 4x - 2
• Data Set B: y = x + 4

For the name plate length problem with the regression equation y = 1.75x + 0.5 given a 22-inch length, we solve for x:

22 = 1.75x + 0.5, which simplifies to x = 12.3 when rounded to the nearest whole number. A reasonable estimate for the number of letters that can fit on the name plate is 12 letters.