Answer:
The y-intercept of the function is: b=10
Step-by-step explanation:
Given the table
x y
1 8
2 6
3 4
4 2
Taking any two points to find the slope
The slope between (1, 8) and (2, 6) is:
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(1,\:8\right),\:\left(x_2,\:y_2\right)=\left(2,\:6\right)[/tex]
[tex]m=\frac{6-8}{2-1}[/tex]
[tex]m=-2[/tex]
We know that the slope-intercept form of the line equation is
[tex]y=mx+b[/tex]
where m is the slope and b is the y-intercept.
Substituting m=-2 and any point i.e. (1, 8) in the slope-intercept form of the line equation to find the y-intercept (b).
[tex]y=mx+b[/tex]
8 = -2(1) + b
8 = -2 + b
b = 8+2
b = 10
Thus, the y-intercept of the function is: b=10
