Write the linear equation that gives the rule for this table. x f(x) 2 27 3 28 4 29 5 30

Question

Write the linear equation that gives the rule for this table.

x f(x)
2 27
3 28
4 29
5 30

Write your answer as an equation with f(x) first, followed by an equals sign.

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Thanh Hà 4 years 2021-08-15T10:52:52+00:00 1 Answers 7 views 0

Answers ( )

  1. thongdat2
    0
    2021-08-15T10:54:26+00:00
    Reply

    Answer:

    The linear equation that gives the rule for this table will be:

    • y=x+25

    Step-by-step explanation:

    Taking two points from the table

    • (2, 27)
    • (3, 28)

    Finding the slope between two points

    \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}

    \left(x_1,\:y_1\right)=\left(2,\:27\right),\:\left(x_2,\:y_2\right)=\left(3,\:28\right)

    m=\frac{28-27}{3-2}

    m=1

    We know the slope-intercept form of linear equation is

    y=mx+b

    where m is the slope and b is the y-intercept

    substituting the point (2, 27) and m=1 in the slope-intercept form to determine the y-intercept ‘b’

    y=mx+b

    27 = 1(2)+b

    27-2 = b

    b = 25

    Now, substituting m=1 and b=25 in the slope-intercept form to determine the linear equation

    y=mx+b

    y=1(x)+25

    y=x+25

    Thus, the linear equation that gives the rule for this table will be:

    • y=x+25

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