manny created a scatter plot and drew a line of best fit, as shown. what is the equation of the line of best…

Explanation:

Step1: Identify the slope-intercept form

The equation of a line is in the form ( y = mx + b ), where ( m ) is the slope and ( b ) is the y-intercept.

Step2: Find the y-intercept (( b ))

From the graph, the line crosses the y-axis at ( (0, 9) )? Wait, no, looking at the graph, when ( x = 0 ), the y-intercept seems to be? Wait, wait, maybe I misread. Wait, the line is drawn, let's check two points. Wait, maybe the y-intercept is 9? Wait, no, let's check the options. Wait, the options have slopes ( 2 ), ( \frac{1}{2} ). Wait, let's calculate the slope. Let's take two points on the line. Let's say when ( x = 0 ), ( y = 9 )? Wait, no, looking at the graph, the line passes through (0,9)? Wait, no, maybe (0,9) and another point. Wait, let's check the options. The options are A: ( y = 2x +7 ), B: ( y=2x +9 ), C: ( y=\frac{1}{2}x +7 ), D: ( y=\frac{1}{2}x +9 ). Wait, let's calculate the slope. Let's take two points. Let's say when ( x = 0 ), ( y = 9 ) (so ( b = 9 )), and when ( x = 2 ), ( y = 10 )? No, wait, maybe the slope is ( \frac{1}{2} )? Wait, no, let's see the direction. Wait, the line is decreasing? Wait, no, the y-axis is on the left, x-axis on the bottom. Wait, maybe I got the axes reversed. Wait, the y-axis is vertical, x-axis horizontal. Wait, the line is going from top left to bottom right? Wait, no, the slope: if x increases, y decreases? Wait, no, the options have positive slopes. Wait, maybe the axes are labeled differently. Wait, the y-axis is labeled with 20 at the top, 0 at the bottom? Wait, no, the graph: the y-axis has 20 at the top, 0 at the bottom, x-axis has 0 at the left, 20 at the right. Wait, so when x increases (moves to the right), y decreases (moves down). Wait, but the options have positive slopes. Wait, maybe I misread the axes. Wait, maybe the y-axis is inverted. Let's check the line of best fit. Let's take two points. Let's say when x = 0, y = 9 (so b = 9), and when x = 2, y = 10? No, that would be slope 0.5. Wait, if x increases by 2, y increases by 1, so slope ( \frac{1}{2} ). And y-intercept 9. So the equation would be ( y = \frac{1}{2}x + 9 ), which is option D? Wait, no, wait the options: D is ( y = \frac{1}{2}x +9 ), B is ( y=2x +9 ), A is ( 2x +7 ), C is ( \frac{1}{2}x +7 ). Wait, maybe I made a mistake. Wait, let's re-express. Let's look at the graph again. The line of best fit: when x=0, y=9 (so b=9), and the slope: let's take two points. Let's say (0,9) and (2,10): slope is ( \frac{10 - 9}{2 - 0} = \frac{1}{2} ). So the equation is ( y = \frac{1}{2}x + 9 ), which is option D? Wait, no, the options: D is ( y = \frac{1}{2}x +9 ), yes. Wait, but let's check the options again. Wait, maybe the slope is ( \frac{1}{2} ) and y-intercept 9. So the correct answer is D? Wait, no, wait the graph: maybe the y-intercept is 9, and slope ( \frac{1}{2} ). So the equation is ( y = \frac{1}{2}x + 9 ), which is option D. Wait, but let's confirm. Alternatively, maybe the slope is 2? No, if slope is 2, then when x increases by 1, y increases by 2. But from the graph, the points are scattered, and the line of best fit: let's see, if x=0, y=9, x=2, y=10 (slope 0.5), x=4, y=11 (slope 0.5), so yes, slope ( \frac{1}{2} ), y-intercept 9. So the equation is ( y = \frac{1}{2}x + 9 ), which is option D. Wait, but the options: D is ( y = \frac{1}{2}x +9 ), yes.

Wait, maybe I messed up the slope. Wait, let's check the line again. If the line passes through (0,9) and (2,10), slope is ( \frac{10 - 9}{2 - 0} = \frac{1}{2} ). So the equation is ( y = \frac{1}{2}x + 9 ), which is option D.

Answer:

D. ( y = \frac{1}{2}x + 9 )