Question

What equation is the rule for the function illustrated by the table of values?

Answer 1

The equation which determined the rule for the function is:

• y = 3x+2

Thus, option B is true.

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)

`\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)`

`\left(x_1,\:y_1\right)=\left(-2,\:-4\right),\:\left(x_2,\:y_2\right)=\left(-1,\:-1\right)`

`m=(-1-\left(-4\right))/(-1-\left(-2\right))`

`m=3`

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:

• y = 3x+2

Thus, option B is true.