Question 849521
<pre>The equation of the line that passes through the 
points (-2,6) and (4,-3) is what?

First we find the slope by using the slope formula:

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

where (x<sub>1</sub>,y<sub>1</sub>) = (-2,6)
and where (x<sub>2</sub>,y<sub>2</sub>) = (4,-3)

m = {{{((-3)-(6))/((4)-(-2))}}}

m = {{{(-9)/(4+2)}}}

m = {{{(-9)/6}}}

m = {{{-3/2}}}

Then we use the

point-slope formula:

y - y<sub>1</sub> = m(x - x<sub>1</sub>)
where (x<sub>1</sub>,y<sub>1</sub>) = (-2,6)

y - 6 = {{{-3/2}}}[x - (-2)]

y - 6 = {{{-3/2}}}(x + 2)

y - 6 = {{{-3/2}}}x - 3
    
    y = {{{-3/2}}}x + 3

Edwin</pre>