Answer:
[tex]y=\dfrac{1}{2}x+8[/tex]
Step-by-step explanation:
The graph of the linear function passes through two given points (-4,6) and (-2,7).
The slope of this linear function is
[tex]\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{7-6}{-2-(-4)}=\dfrac{1}{2}[/tex]
Thus, the equation of the function is
[tex]y=\dfrac{1}{2}x+b[/tex]
Substitute coordinates of the first point:
[tex]6=\dfrac{1}{2}\cdot (-4)+b\\ \\6=-2+b\\ \\b=6+2\\ \\b=8[/tex]
Hence,
[tex]y=\dfrac{1}{2}x+8[/tex]
