Question 70332
Write the standard form of an equation of the  line that passes through each pair of points:

(-5,7), (0,1/2)
In order to find the equation of a line, you need a point an a slope.  You don't have a slope, but never fear, you have two points and can get the slope using the slope formula:
{{{highlight(m=(y[2]-y[1])/(x[2]-x[1]))}}}, where m=slope, and (x1,y1) and (x2,y2) are your given points.
(x1,y1)=(-5,7) and (x2,y2)=(0,1/2)
{{{m=(1/2-7)/(0-(-5))}}}
{{{m=(1/2-14/2)/5}}}
{{{m=(-13/2)/5}}}
{{{m=(-13/2)(1/5)}}}
{{{m=-13/10}}}
Now you have a point and a slope, so you can use the point slope formula to find the equation of the line:  {{{highlight(y-y[1]=m(x-x[1]))}}}, where m=slope and (x1,y1) is a given point.
(x1,y1)=(-5,7) and m=-13/10
{{{y-7=(-13/10)(x-(-5))}}}
{{{y-7=(-13/10)(x+5)}}}
The Standard form of a line is {{{highlight(Ax+By=C)}}}, where A, B, and C are integers. A lot of books and teachers also require A to be positive.
{{{10(y-7)=10(-13/10)(x+5)}}}
{{{10y-70=-13(x+5)}}}
{{{10y-70=-13x-65}}}
{{{13x+10y-70=13x-13x-65}}}
{{{13x+10y-70+70=-65+70}}}
{{{highlight(13x+10y=5)}}}
Happy Calculating!!!