The scatter plot above shows the number of pages read compared to the number of hours read. Which linear equation below supports the best fit line on the scatter plot above?

Question

y = 20x

y = 2x

y = x + 20

y = 20x + 20

Answer 1

To determine which linear equation best fits the line in the scatter plot comparing the number of pages read (y) to the number of hours read (x), we should consider the slope and y-intercept of each equation.

1. y = 20x: This has a slope of 20 and a y-intercept of 0, indicating that for every hour read, 20 pages are read.

2. y = 2x: This has a slope of 2 and a y-intercept of 0, indicating that for every hour read, only 2 pages are read.

3. y = x + 20: This has a slope of 1 and a y-intercept of 20, indicating that for every hour read, 1 page is read, and there are also 20 additional pages.

4. y = 20x + 20: This has a slope of 20 and a y-intercept of 20, meaning that for every hour read, 20 pages are read, plus an initial 20 pages.

To identify the best fit, consider the pattern of the data on the scatter plot: if the points seem to increase steeply, a steeper slope (like 20) might be appropriate. If the line intersects the y-axis at a significant value greater than 0, then an equation with a y-intercept (like 20) might be needed.

If the plot suggests a high number of pages relative to the hours, options like y = 20x or y = 20x + 20 are more likely to be valid.

Without seeing the actual scatter plot, it's difficult to give a definitive answer, but based on typical patterns:

• If there's no initial offset, y = 20x may be correct.
• If an initial number of pages is read before starting the hours, then y = 20x + 20 would likely fit better.

You would need to visually analyze the scatter plot to make a more precise determination.

Answer 2

17 dots and its going straight up the the right corner

Answer 3

Given the description that there are 17 dots in a scatter plot that trend straight up toward the right corner, this suggests a strong positive correlation between the number of pages read (y-axis) and the number of hours read (x-axis).

Now, let’s analyze the equations again, considering that the points move upward rapidly:

1. y = 20x: This indicates a slope of 20, meaning for every hour read, 20 pages are read. This would create a steep upward trend.

2. y = 2x: This indicates a slope of 2, which would be a much gentler slope.

3. y = x + 20: This means for every hour, 1 additional page is read with a starting point of 20 pages. This slope is also relatively shallow.

4. y = 20x + 20: This indicates a slope of 20 with an intercept of 20, meaning we start with 20 pages and then read 20 more for every additional hour.

Since you mentioned the points are "going straight up to the right corner" and likely have a steep slope, the best fitting equation would be:

y = 20x if there is no initial number of pages read before starting.

If you suspect that there are some pages read at the beginning (before any hours are logged), then y = 20x + 20 might be the best choice.

However, from your statement that it goes straight up toward the right and assuming there's no offset at the start, y = 20x would likely be the best fit. If there's a notable starting point (like an initial 20 pages), then y = 20x + 20 would be suitable.

In essence:

• y = 20x is best for a direct, steep correlation.
• y = 20x + 20 is best if there's a noticeable starting volume of pages.

Without more specific context about initial pages, y = 20x sounds most in line with your description of the scatter plot.