Question 694619
the relationship between {{{x}}} and {{{f(x)}}} for the following

{{{f(x)=ax+b}}} or {{{y=ax+b}}}

given:

 input           output

{{{x}}}...........{{{f(x)}}} or {{{y}}}
{{{-1}}}            {{{ 3}}}
{{{0}}}                {{{2}}}
{{{1}}}                {{{1}}}

so, you are given three points which you can plot on a Cartesian coordinate system and graph a line that contains these points

({{{x}}},{{{y}}})= ({{{-1}}},{{{3}}})

({{{x}}},{{{y}}})= ({{{0}}},{{{2}}})...this is {{{y-intercept}}}

({{{x}}},{{{y}}})= ({{{1}}},{{{1}}})

now we can find the equation of a line passing through these points

*[invoke find_equation_of_line 1, 1, 0, 2]

so,the equation of a line passing through these points is {{{y=-x+2}}} where {{{a=-1}}} and {{{b=2}}}

now we can check if all three given points lie on this line


{{{drawing(600,600,-10,10,-10,10,grid(1),circle(-1,3,0.2),circle(1,1,0.2),circle(0,2,0.2),graph(600,600,-10,10,-10,10,-x+2))}}}

as you can see, all three given points do lie on this line