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What is the standard form of an equation of the line that passes through the points (3,0) (6,-8)?

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1 Answer

Hi Mikk;
Standard form of an equation is...
Ax+By=C, neither A nor B equal zero, and A is greater than zero.
Let's begin by establishing slope.  This is represented as m, and is the change-of-y divided by the change-of-x.
m=(y-y1)/(x-x1)
m=(0--8)/(3-6)
Subtracting a negative number is the same as adding a positive number.
m=(0+8)/(3-6)
m=(8)/(-3)
m=-8/3
(3,0) is the y-intercept.  This is the value of y when x=0.  Therefore, let's proceed with the slope-intercept form.  This is...
y=mx+b, b is the y-intercept, the value of x when y=0.
y=(-8/3)x+3
Let's convert to standard form.  We will add (8/3)x to both sides...
(8/3)x+y=(8/3)x-(8/3)x+3
 
(8/3)x+y=3