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Write an equation for each linear function described. Show your work. The graph of the function passes through the point (2,1), and y increases by 4 when x increases by 1.

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Explanation:

As

  • The graph of the function passes through the point (2,1), and
  • y increases by 4 when x increases by 1.

so

x y

2 1

3 5

4 9

5 13

6 17

and so on

From the table:


\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=(y_2-y_1)/(x_2-x_1)


\left(x_1,\:y_1\right)=\left(2,\:1\right),\:\left(x_2,\:y_2\right)=\left(3,\:5\right)


m=(5-1)/(3-2)


m=4

As the slope-intercept form of the line is


y=mx+b

putting m=4 and any point, let say (2, 1) to find y-intercept 'b'.


1=\left(4\right)2+b


8+b=1


8+b-8=1-8


b=-7

So putting
b=-7 and
m=4 in the slope-intercept form of the line


y=\left(4\right)x+\left(-7\right)


y=4x-7

Therefore, the equation for the linear function will be:


y=4x-7

User Joline
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