Question

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.

Answer 1

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`