Question 214303
Find the equation of the line that passes through the two points (3,11) and (6,20)
Since you don't specify the form of equation you need, I'll assume that the "slope-intercept" form (y = mx+b) is acceptable.
Start by finding the slope (m) of the line using the two given points.
{{{m = (y[2]-y[1])/(x[2]-x[1])}}} where:{{{x[1] = 3}}}, {{{y[1] = 11}}}, {{{x[2] = 6}}}, and {{{y[2] = 20}}} Making the appropriate substitutions, we get:
{{{m = (20-11)/(6-3)}}}
{{{m = 9/3}}}
{{{m = 3}}}
So you can start out with:
{{{y = 3x+b}}} To find the value of b, the y-intercept, substitute the x- and y-coordinates of either one of the two given points. Using the first point (3,11) we have:
{{{11 = 3(3)+b}}}
{{{11 = 9+b}}} Subtract 9 from both sides.
{{{2 = b}}}
The final equation is:
{{{highlight(y = 3x+2)}}}