Question 107812
The slope intercept form is {{{y = mx + b}}}
m is the slope, b is the y-intercept
Each point is a solution to the equation
(5,6)
{{{6 = m*5 + b}}}
(-7,3)
{{{3 = m*(-7) + b}}}
now solve for m and b
multiply the 2nd equation by -1 and add to the 1st
{{{3 = m*(-7) + b}}}
{{{-3 = m*7 - b}}}
add to
{{{6 = m*5 + b}}}
{{{3 = m*12}}}
{{{m = 1/4}}}
Now find b, by substitution in either equation-I'll use 1st
{{{6 = (1/4)*5 + b}}}
multiply both sides by 4
{{{24 = 5 + 4b}}}
{{{4b = 19}}}
{{{b = 19/4}}}
So, the equation is {{{y = (1/4)*x + 19/4}}}
Check answer by seeing if it goes through both points
{{{6 = (1/4)*5 + 19/4}}}
{{{6 = 5/4 + 19/4}}}
{{{24/4 = 24/4}}} OK
also
{{{3 = (1/4)*(-7) + 19/4}}}
{{{3 = -(7/4) + 19/4}}}
{{{12/4 = 12/4}}} OK