Question 779455
<pre>
 ((((1/2,3/5) and (- 1/4,2/5))))

First we use the 
slope formula:
m = {{{(y[2]-y[1])/(x[2]-x[1])}}}
where (x<sub>1</sub>,y<sub>1</sub>) = ({{{1/2}}},{{{3/5}}})
and where (x<sub>2</sub>,y<sub>2</sub>) = ({{{-1/4}}},{{{2/5}}})
Substituting in the slope formula

m = {{{((2/5)-(3/5))/((-1/4)-(1/2))}}} = {{{(-1/5)/((-1/4)-(2/4))}}} = {{{(-1/5)/(-3/4)}}} = {{{(1/5)/(3/4)}}} = {{{1/5}}}÷{{{3/4}}} = {{{1/5}}}·{{{4/3}}} = {{{4/15}}}  

Next 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>) = ({{{1/2}}},{{{3/5}}})

y - {{{3/5}}} = {{{4/15}}}(x - {{{1/2}}})

Now we solve for y:

Distribute on the right:

y - {{{3/5}}} = {{{4/15}}}x - {{{4/15}}}·{{{1/2}}}

              {{{2}}}
y - {{{3/5}}} = {{{4/15}}}x - {{{cross(4)/15}}}·{{{1/cross(2)}}}

y - {{{3/5}}} = {{{4/15}}}x - {{{2/15}}}

Add {{{3/5}}} to both sides:

y = {{{4/15}}}x - {{{2/15}}} + {{{3/5}}} 

The least common denominator for the last two terms is 15.
So we write {{{3/5}}} as {{{9/15}}}

y = {{{4/15}}}x - {{{2/15}}} + {{{9/15}}}

y = {{{4/15}}}x + {{{7/15}}}  

Edwin</pre>