Question 178719
{{{y}}} is a function of {{{x}}}, or
{{{y = f(x)}}}
given:
{{{1 = f(1)}}}
{{{y = 1}}}
{{{x = 1}}}
This gives me the point (1,1)
{{{10 = f(4)}}}
{{{y = 10}}}
{{{x = 4}}}
This gives me the point (4,10)
{{{f(x) = mx + b}}}
{{{y = f(x)}}}
{{{y = mx + b}}}
For the point (1,1):
(1) {{{1 = m*1 + b}}}
For the point (4,10):
(2) {{{10 = m*4 + b}}}
Multiply (1) by {{{4}}} and subtract from (2)
(2) {{{10 = 4m + b}}}
(1) {{{-4 = -4m - 4b}}}
{{{6 = -3b}}}
{{{b = -2}}}
Substitute this in (1)
(1) {{{1 = m*1 + b}}}
{{{1 = m - 2}}}
{{{m = 3}}}
The equation is {{{f(x) = 3x - 2}}} answer 

check:
does it go through (1,1)?
{{{1 = 3*1 - 2}}}
{{{1 = 1}}}
OK
Does it go through (4,10)?
{{{10 = 3*4 - 2}}}
{{{10 = 10}}}
OK