The scatterplot shows the number of minutes spent reading (x) and the number of pages read (y) by each of seven students last night. Use the labeled points to create a linear model that predicts the number of pages that a typical student reads in x minutes. Which equation represents this linear model?
No scatterplot. Cannot copy and paste here.
The scatterplot shows the number of minutes spent reading (x) and the number of pages read (y) by each of seven students last night. Use the labeled points to create a linear model that predicts the number of pages that a typical student reads in x minutes. Which equation represents this linear model?
To create a linear model, we need to find the equation of the line that best fits the given scatterplot.
Looking at the scatterplot, we can see that there is a positive linear relationship between the number of minutes spent reading (x) and the number of pages read (y). As the number of minutes increases, the number of pages read also tends to increase.
To find the equation of the line, we can use the method of least squares regression. This method finds the line that minimizes the sum of the squared differences between the observed y-values and the predicted y-values on the line.
Using the labeled points on the scatterplot, we can determine the line that best represents the data. Once we have the line, we can write its equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
Let's find the equation step-by-step:
1. Identify two points on the line:
From the scatterplot, let's choose two points:
Point 1: (20, 30) and Point 2: (40, 50)
2. Determine the slope (m) using the formula:
Slope (m) = (Change in y) / (Change in x)
m = (50 - 30) / (40 - 20)
m = 20 / 20
m = 1
3. Use one of the points and the slope to find the y-intercept (b):
Using Point 1 (20, 30):
y = mx + b
30 = 1(20) + b
30 = 20 + b
b = 10
4. Write the equation in slope-intercept form:
y = mx + b
y = 1x + 10
Therefore, the equation that represents the linear model for predicting the number of pages read in x minutes is:
y = x + 10
To create a linear model that predicts the number of pages that a typical student reads in x minutes, we need to find a line of best fit for the given scatterplot. This line should pass through the middle of the plotted points.
To find the equation of this line, we can use the method of least squares regression. This involves finding the slope and y-intercept of the line that minimizes the sum of the squared vertical distances between the data points and the line.
Here's how you can find the equation representing the linear model:
1. Identify two points that lie along or close to the line of best fit. In this case, we can use the labeled points on the scatterplot.
2. Determine the coordinates of these two points. Let's say we choose the points (x1, y1) and (x2, y2).
3. Calculate the slope of the line using the formula:
slope = (y2 - y1) / (x2 - x1)
4. Calculate the y-intercept of the line using the formula:
y-intercept = y1 - slope * x1
5. Substitute the values of the slope and y-intercept obtained from steps 3 and 4 into the equation form y = mx + b, where m is the slope and b is the y-intercept.
6. Simplify the equation, if possible, to obtain the linear model equation that predicts the number of pages read in x minutes.
By following these steps using the information given in the scatterplot, you can determine the equation that represents the linear model.