Question

Consider the line that passes through each pair of given points, and decide what type of slope the line has.(-7,8) and (-7,0) Zero slope(6,-3) and (-4,-3) Positive slope(2,4) and (5,1) negative slope(3,5) and (-1,2) undefined slope

Answer 1

For each of the pairs of points, we calculate the slope.

$\text{Slope}=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}}$

(a)(-7,8) and (-7,0)

$\begin{gathered} \text{Slope}=\frac{8-0}{-7-(-7)}=\frac{8}{-7+7} \\ =\frac{8}{0} \\ =\text{Undefined} \end{gathered}$

The slope of the line joining the points (-7,8) and (-7,0) is undefined.

(b)(6,-3) and (-4,-3)

$\begin{gathered} \text{Slope}=\frac{-3-(-3)}{6-(-4)} \\ =\frac{0}{10} \\ =0 \end{gathered}$

The slope of the line joining the points (6,-3) and (-4,-3) is zero.

(c)(2,4) and (5,1)

$\begin{gathered} \text{Slope}=\frac{2-5}{4-1} \\ =\frac{-3}{3} \\ =-1 \end{gathered}$

The slope of the line joining the points (2,4) and (5,1) is negative.

(d)(3,5) and (-1,2)

$\begin{gathered} \text{Slope}=\frac{3-(-1)}{5-2} \\ =\frac{4}{3} \end{gathered}$

The slope of the line joining the points (3,5) and (-1,2)) is positive.