Question

use the graph of the scatter plot to answer the question.
based on the graph, what would be the slope for the line of best fit of the scatter plot?
a. 0
b. \\(\frac{1}{2}\\)
c. 1
d. \\(1\frac{1}{2}\\)
e. 2

Explanation:

Step1: Analyze the scatter plot trend

The scatter plot shows a positive linear trend. To find the slope of the line of best fit, we can observe the general rise over run.

Step2: Estimate slope using points

Pick two approximate points on the line of best fit. For example, when \( x = 0 \), \( y\approx0 \); when \( x = 2 \), \( y\approx2 \). The slope formula is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Using \( (0,0) \) and \( (2,2) \), \( m=\frac{2 - 0}{2 - 0}=1 \). Wait, but let's check another pair. If \( x = -4 \), \( y\approx - 4 \); \( x = 4 \), \( y\approx4 \). Then \( m=\frac{4 - (-4)}{4 - (-4)}=\frac{8}{8}=1 \). Wait, but maybe I misread. Wait, no, let's check the options. Wait, maybe another approach. The line of best fit seems to have a slope where for each unit increase in x, y increases by 1? Wait, no, wait the options include 1 (option C), 1.5 (D), 2 (E), 0.5 (B), 0 (A). Wait, maybe my initial points are wrong. Let's look at the graph again. The points are clustered such that when x increases by 2, y increases by 2? No, wait, when x goes from -4 to 4 (8 units), y goes from -4 to 4 (8 units), so slope is 1. But wait, maybe the correct slope is 1? Wait, no, wait the options: C is 1, D is \( 1\frac{1}{2} \), E is 2. Wait, maybe I made a mistake. Wait, let's take two points: (0,0) and (2,2) – slope 1. (1,1) and (3,3) – slope 1. So the slope should be 1? Wait, but let's check the options. Option C is 1. Wait, but maybe the correct answer is C? Wait, no, wait the graph: when x increases by 1, y increases by 1? Let's see, from x=-1, y=-1 to x=0, y=0: slope 1. From x=0, y=0 to x=1, y=1: slope 1. So the line of best fit has a slope of 1.

Answer:

C. 1