Question

Mary was told that a line goes through the points (1, 3) and (6, -2) and has a slope of 3. A. Explain why the information Mary was given cannot be correct. B. If the given point (1, 3) and the given slope are correct, what is the equation for the line? C. Give the coordinates of another point on the line. D. If the given points are correct on the line, what is the slope? E. Write an equation for the line.

Answer 1

Below in bold.

Explanation:

A. We can calculate the slope using (y2 - y1) / (x2 - x1)

= (3 - (-2)) / (1 - 6)

= 5/-5

= -1.

So the given slope of 3 or one of the points is NOT correct.

B. If the point (1, 3 ) and the slope are correct then the equation for the line (using the point-slope form) is y - 3 = 3(x - 1)

C Another point on this line would be , when x = 0 , y = 3*-1 + 3 = 0

so it's (0, 0)

D. If the given points are correct the slope is ( as above) = -1.

E. The equation for this line is

y - 3 = -1(x - 1)

y = -x + 1 + 3

y = 4 - x.