Question 59522
Find the equation for this line (1,4)(5,6)
In order to find the equation for a line you need the slope and a point.  
You don't have a slope, so we need to find it using the slope formula {{{highlight(m=(y2-y1)/(x2-x1))}}}, m=slope, (x1,y1) and (x2,y2) are given points.
(x1,y1)=(1,4) and (x2,y2)=(5,6)
{{{m=(6-4)/(5-1)}}}
{{{m=2/4}}}
{{{m=1/2}}}
Now we can use the point slope formula {{{highlight(y-y1=m(x-x1))}}},m=slope, and (x1,y1) is a given point.
m=1/2 and (x1,y1)=(1,4)
{{{y-4=(1/2)(x-1)}}}
{{{y-4=(1/2)x-(1/2)}}}
{{{y-4+4=(1/2)x-(1/2)+4}}}
{{{y=(1/2)x-1/2+8/2}}}
{{{y=(1/2)x+7/2}}}  Slope intercept form of the line.
{{{2y=2(1/2)x+2(7/2)}}}
{{{2y=x+7}}}
{{{-x+2y=-x+x+7}}}
{{{-x+2y=7}}}
{{{-(-x+2y)=-7}}}
{{{x-2y=-7}}}  Standard form of a line.
Happy Calculating!!!