Question

examine lines a, b, c, and d on the graph at right. for each line, decide if the slope is positive, negative, or zero. then draw and label slope triangles on your resource page and calculate the slope of each line.

Explanation:

Step1: Determine slope sign for line A

As x - value increases, y - value decreases, so slope is negative.
Let two points on line A be (-6,6) and (0,3).
The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$.
$m_A=\frac{3 - 6}{0-(-6)}=\frac{-3}{6}=-\frac{1}{2}$

Step2: Determine slope sign for line B

As x - value increases, y - value increases, so slope is positive.
Let two points on line B be (-3,0) and (0,6).
$m_B=\frac{6 - 0}{0-(-3)}=\frac{6}{3}=2$

Step3: Determine slope sign for line C

As x - value increases, y - value increases, so slope is positive.
Let two points on line C be (0,3) and (6,6).
$m_C=\frac{6 - 3}{6 - 0}=\frac{3}{6}=\frac{1}{2}$

Step4: Determine slope sign for line D

As x - value changes, y - value remains the same, so slope is zero.
Let two points on line D be (-6,3) and (6,3).
$m_D=\frac{3 - 3}{6-(-6)}=\frac{0}{12}=0$

Answer:

Line A: Slope is negative, $m =-\frac{1}{2}$
Line B: Slope is positive, $m = 2$
Line C: Slope is positive, $m=\frac{1}{2}$
Line D: Slope is zero, $m = 0$