Question

what is the slope of the line of best-fit in the scatterplot below? the scatterplot has points (3,12), (6,19) and a grid. the options are \\(\frac{9}{27}\\), \\(\frac{3}{7}\\), \\(\frac{7}{3}\\), \\(\frac{27}{9}\\).

Explanation:

Step1: Recall slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Identify two points on the line

We have points \((3, 12)\) and \((6, 19)\) on the line of best - fit. Let \((x_1,y_1)=(3,12)\) and \((x_2,y_2)=(6,19)\).

Step3: Calculate the slope

Substitute into the slope formula: \( m=\frac{19 - 12}{6 - 3}=\frac{7}{3} \)? Wait, no, wait. Wait, maybe I made a mistake. Wait, let's check the graph again. Wait, maybe the points are (3,12) and (6,19)? Wait, 19 - 12 = 7, 6 - 3 = 3, so \( \frac{7}{3} \)? But wait, let's check the other way. Wait, maybe the points are (3,12) and (6,19). Wait, but let's see the options. Wait, maybe I misread the points. Wait, the point (6,19) and maybe another point. Wait, no, let's recalculate. Wait, 19 - 12 = 7, 6 - 3 = 3, so slope is \( \frac{7}{3} \)? Wait, but let's check the options. The options are \( \frac{9}{27}=\frac{1}{3} \), \( \frac{3}{7} \), \( \frac{7}{3} \), \( \frac{27}{9} = 3 \). Wait, maybe the points are (3,12) and (6,19). So \( y_2 - y_1=19 - 12 = 7 \), \( x_2 - x_1=6 - 3 = 3 \), so slope is \( \frac{7}{3} \).
Wait, no, wait, maybe I made a mistake. Wait, let's check the y - values. Wait, 12 to 19 is an increase of 7, x from 3 to 6 is an increase of 3. So slope is \( \frac{7}{3} \).

Answer:

\(\frac{7}{3}\) (corresponding to the option \(\frac{7}{3}\))