Question

What is an equation of the line that passes through the points (2,1) and (6,-5)?

Answer 1

The equation will be in the form y=mx+b, where m is the slope of the line and b is the y-intercept (value of y when x is 0).

The slope can be found by dividing the difference in two y-values of points on the line by the difference in the corresponding two x-values.  In this case, we have (1-(-5))/(2-6), or 6/-4, or -3/2.  Therefore, our equation can now be expressed as y=(-3/2)x+b.

Substituting in (2, 1) for this equation, we see that:

3+b=1

Adding 3, we see that b=4.  Therefore, our final equation is y=(-3/2)x+4.