<PRE><B>Question 784972</B>
Q: Using the formula y= mx+b find the equation of the line determined by the two points (-3,2) and (-2, 8).
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A:
If ({{{x[1]}}}, {{{y[1]}}}) and ({{{x[2]}}}, {{{y[2]}}}) are points on the line, then the slope of the line is m = {{{(y[2] - y[1])/(x[2] - x[1])}}}.
The slope of the line containing (-3,2) and (-2, 8) is
m = {{{(8 - 2)/(-2 - (-3))}}} = 6.
The equation of the line is y = 6x + b, where b is the y-intercept.
To solve for the value of b, choose any point on the line.
If we choose (-3, 2), then substitute x = -3, y = 2, and solve for b.
y = 6x + b
2 = 6(-3) + b
b = 2 + 18 = 20
Therefore, the equation of the line is {{{highlight(y = 6x + 20)}}}.</PRE>