Question

Write a linear function f with f(0)=7 and f(3)=1.

Answer 1

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a = ( 0 , 7 ) & b = ( 3 , 1 )

First need to find the slope using the following equation :

`slope = (y(b) - y(a))/(x(b) - x(a)) \\`

`slope = (1 - 7)/(3 - 0) \\`

`slope = ( - 6)/(3) \\`

`slope = - 2`

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We have following equation to find the point-slope form of the linear functions using the slope and one of the through points .

`y - y(0) = m * ( \: x - x(0) \: )`

`x(0) = x - coordinate \: \: of \: \: through \: \: point \\`

`y(0) = y - coordinate \: \: of \: \: through \: \: point \\`

`m = slope`

I choose point (( a )) to put in the equation.

`y - 7 = - 2 * (x - 0)`

`y - 7 = - 2x + 0`

`y - 7 = - 2x`

Add sides 7

`y - 7 + 7 = - 2x + 7`

`y = - 2x + 7`

This the slope-intercept form .

Done...

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