Question 1175139

write a linear function f with the given values


A. 
{{{f(x) = ax+b}}}

if {{{f(0) = 4}}} means for {{{x=0}}} {{{y=4}}}
{{{4= a*0+b}}}
{{{b=4}}}

if f(5) = 19
{{{19= a*5+4}}}
{{{19-4= 5a}}}
{{{15= 5a}}}
{{{a=3}}}

equation is: {{{f(x) = 3x+4}}}

B. 
use another way to find equation

if {{{f (-5) = 32}}}, that is point ({{{x[1]}}},{{{y[1]}}})=({{{-5}}},{{{32}}})

if {{{f(0) = 22}}}, that is point ({{{x[2]}}},{{{y[2]}}})=({{{0}}},{{{22}}})=> this point is y-intercept, so {{{b=22}}}

now find a slope {{{a}}}

{{{a=(y[2]-y[1])/(x[2]-x[1])}}}

{{{a=(22-32)/(0-(-5))}}}

{{{a=-10/5}}}

{{{a=-2}}}

equation is: {{{f(x) = -2x+22}}}