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

What Equation Is The Rule For The Function Illustrated By The Table Of Values class=

Sagot :

absor201

Answer:

The equation which determined the rule for the function is:

  • y = 3x+2

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:

  • y = 3x+2

Thus, option B is true.

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