Answer:
The equation which determined the rule for the function is:
Thus, option B is true.
Step-by-step explanation:
We know the slope-intercept form of line function is
y = mx+b
where m is the slope and b is the y-intercept
Given the table
x -2 -1 0 1 2
y -4 -1 2 5 8
Finding the slope between the points (-2, -4) and (-1, -1)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-2,\:-4\right),\:\left(x_2,\:y_2\right)=\left(-1,\:-1\right)[/tex]
[tex]m=\frac{-1-\left(-4\right)}{-1-\left(-2\right)}[/tex]
[tex]m=3[/tex]
Thus, the slope of the function = m = 3
We know that the y-intercept can be determined by setting x = 0 and determining the corresponding y-value.
It is clear,
at x=0, y = 2
Thus, the y-intercept 'b' = 2
now substituting m = 3 and b =2 in the slope-intercept form
y = mx+b
y = 3x + 2
Therefore, the equation which determined the rule for the function is:
Thus, option B is true.
