Answer:
[tex]y=\frac{1}{2}x+7[/tex]
Step-by-step explanation:
Let's analyze each case.
case A) [tex]y=3x[/tex]
This equation represent a direct variation and the relationship shown in the scatter plot does not passes through the origin
therefore
The equation case A) could not represent the relationship shown in the scatter plot
case B) [tex]y=\frac{5}{2}x-1[/tex]
The y-intercept of this equation is equal to [tex]-1[/tex] and the relationship shown in the scatter plot does not have points with negative y-coordinates
therefore
The equation case B) could not represent the relationship shown in the scatter plot
case C) [tex]y=\frac{1}{2}x+7[/tex]
The y-intercept of this equation is equal to [tex]7[/tex] and the relationship shown in the scatter plot has points with nearest coordinates
therefore
The equation case C) could represent the relationship shown in the scatter plot
case D) [tex]y=-x+8[/tex]
This equation has a slope negative and the relationship shown in the scatter plot has a positive slope
therefore
The equation case D) could not represent the relationship shown in the scatter plot
