Question 983358

We are trying to find equation of form {{{y=ax+b}}}, where {{{a}}} is slope, and {{{b}}} is intercept, which passes through points ({{{x[1]}}}, {{{y[1]}}}) = ({{{7}}}, {{{66}}}) and ({{{x[2]}}}, {{{y[2]}}}) = ({{{1}}}, {{{18}}}).
Slope {{{a }}}is:

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

{{{ a=(18-66)/(1-7)}}}

{{{ a=(-48)/(-6)}}}

{{{ a=8}}}

Intercept is found from equation 
{{{a*x[1]+b=y[1]}}}, or 

{{{8*7+b=66}}}
{{{56+b=66}}}

{{{b=66-56}}}

From that,
intercept {{{b}}} is 

{{{b=10}}}
 
so, your equation is

{{{y=8x + 10}}}...or, in standard form

{{{-10=8x -y}}} or, switch sides

{{{8x -y=-10}}}


and your answer is:

{{{b. 8x-y=-10}}}


{{{drawing( 600, 600, -10, 10, -10, 70, 
circle(7,66,.12),circle(1,18,.12),
locate(7,66,p(7,66)),locate(1,18,p(1,18)),
 graph( 600, 600, -10, 10, -10, 70, 8x + 10)) }}}