Question

Examine the following table of points, which are all on a certain line.

x y

−2 4

0 2

1 1

3 −1



What is the slope of this line? Enter your answer as a number, like this: 42, or, if the slope is undefined, enter the lowercase letter "u".

Answer 1

`\bf \begin{array}cc \cline{1-2} x&y\\ \cline{1-2} {-2}~~\ast&{4}~~\ast\\ 0&2\\ 1&1\\ {3}~~\ast&{-1}~~\ast\\ \cline{1-2} \end{array}~\hspace{10em} (\stackrel{x_1}{-2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-1-4}{3-(-2)}\implies \cfrac{-5}{3+2}\implies \cfrac{-5}{5}\implies -1`

Answer 2

The slope of this line is -1.

The slope formula is useful:

m = (y2 -y1)/(x2 -x1)

where:

m is the slope of the line

y1 and y2 are the y-coordinates of two points on the line

x1 and x2 are the x-coordinates of the two points on the line

m = (2 -4)/(0 -(-2)) = -2/2 = -1

The slope of this line is -1.

The points on the line drop 1 unit for each 1 unit to the right.

m = rise/run = -1/1 = -1