Question 106865
find the {{{slope}}} of the line that passes through ({{{-3}}},{{{1}}}) and ({{{2}}},{{{-6}}}).

{{{slope = (change_in_y/change_in_x)}}}

If {{{slope = m}}},  {{{change_in_y = y[2] – y[1]}}}, {{{change_in_x = x[2] – x[1]}}}, then we have:

m =(y[2] – y[1])/(x[2] – x[1])

Since 
{{{x[1] =-3}}}
{{{x[2] =2}}}
{{{y[1] =1}}}
{{{y[2] =-6}}}


we will have:

m = (-6– 1)/(2 – (-3))

{{{m = -7/(2 + 3)}}}


{{{m = -(7/5)}}}

We are trying to find equation {{{y = ax + b}}}. 
The value of slope {{{a = -7/5}}} is already given to us, as a point ({{{-3}}},{{{1}}}) that lies on the line as well.

we need {{{b}}} which is:
{{{b = y[1]}}} – {{{(ax[1])}}}

{{{b = 1 - (-7/5(-3))}}}

{{{b = 1 -(21/5)}}}
{{{b = (5-21)/5}}}
{{{b= -(16/5)}}}

so,
{{{y = ax + b}}} will be:

{{{y = -(7/5)x - 16/5}}} 

here is the graph of this function, make sure that both given points ({{{-3}}},{{{1}}}) and ({{{2}}},{{{-6}}})lie on line.


*[invoke graphing_linear_equations "slope-intercept", 1, 2, 3, -7/5, -16/5]