Answer:
B
Step-by-step explanation:
To find the equation of the line, let's pick two points from the table.
We can use (-2, 1) and (4, 4).
First, find the slope of the line. So:
[tex]\displaystyle m=\frac{4-1}{4-(-2)}=\frac{3}{6}=\frac{1}{2}[/tex]
Next, we can use the slope-intercept form given by:
[tex]y=mx+b[/tex]
Since the slope is 1/2:
[tex]\displaystyle y=\frac{1}{2}x+b[/tex]
Since we know that the line passes through the point (4, 4), y = 4 when x = 4. Therefore:
[tex]\displaystyle (4)=\frac{1}{2}(4)+b[/tex]
Solve for b. Multiply:
[tex]4=2+b[/tex]
So:
[tex]b=2[/tex]
Therefore, our equation is:
[tex]\displaystyle y=\frac{1}{2}x+2[/tex]
Our answer is B.
