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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.

Respuesta :

SaniShahbaz

Step-by-step 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:

[tex]\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]

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

[tex]m=\frac{5-1}{3-2}[/tex]

[tex]m=4[/tex]

As the slope-intercept form of the line is

[tex]y=mx+b[/tex]

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

[tex]1=\left(4\right)2+b[/tex]

[tex]8+b=1[/tex]

[tex]8+b-8=1-8[/tex]

[tex]b=-7[/tex]

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

[tex]y=\left(4\right)x+\left(-7\right)[/tex]

[tex]y=4x-7[/tex]

Therefore, the equation for the linear function will be:

[tex]y=4x-7[/tex]

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