Question

A family of linear functions is given by
$f\left(x\right)=mx+(3-2m)$
where $x$ is the independent variable and $m$ is a constant.
(a) Graph $f$ for $m=0,1,2,-3$ and $-5$
(b) What do all the graphs in part (a) have in common
(c) Write the equation of the family of functions whose graphs pass by the same point.

Answer 1

(b) all the graph meets at common point $(2,3)$

Equation of family of line from $(-2,-4)$ and have same common point $(2,3)$

$y+4=\frac{3+4}{2+2}(x+2)$

$4y+16=7x+14$

$4y=7x-2$

(c)

Here the slope of family of functions should be equal to slope of family of line $m=\frac{7}{4}$

$f\left(x\right)=\frac{7}{4}x+(3-\frac{7}{2})$

$f\left(x\right)=\frac{7}{4}-\frac{1}{2}$