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 :

$slope = \frac{y(b) - y(a)}{x(b) - x(a)}$

$slope = \frac{1 - 7}{3 - 0}$

$slope = \frac{ - 6}{3}$

$slope = - 2$

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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 .

$y - y(0) = m \times ( \: x - x(0) \: )$

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

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

$m = slope$

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

$y - 7 = - 2 \times (x - 0)$

$y - 7 = - 2x + 0$

$y - 7 = - 2x$

Add sides 7

$y - 7 + 7 = - 2x + 7$

$y = - 2x + 7$

This the slope-intercept form .

Done...

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