Answer:
The first relationship has a zero slope
Step-by-step explanation:
Each line crosses two point A(x1; y1); B(x2; y2)
We have the formula to calculate the slope of a straight line is:
Slope = [tex]\frac{y2-y1}{x2-x1}[/tex]
1. The line reflecting the first relationship crosses two points (x1 = -3; y1 = 2) and (x2 = -1; y2 = 2)
=> Slope of the first relationship is: [tex]\frac{y2-y1}{x2-x1}[/tex] = [tex]\frac{2-2}{-1-(-3)}[/tex] = 0
2. The line reflecting the second relationship crosses two points (x1 = -3; y1 = 3) and (x2 = -1; y2 = 1)
=> Slope of the second relationship is: [tex]\frac{y2-y1}{x2-x1}[/tex] = [tex]\frac{1-3}{-1-(-3)}[/tex] = -1
3. The line reflecting the third relationship crosses two points (x1 = 0; y1 = 0) and (x2 = 1; y2 = 1)
=> Slope of the third relationship is: [tex]\frac{y2-y1}{x2-x1}[/tex] = [tex]\frac{1-0}{1-0}[/tex] = 1
4. The line reflecting the third relationship crosses two points (x1 = -2; y1 = 0) and (x2 = -2; y2 = 1)
=> Slope of the third relationship is: [tex]\frac{y2-y1}{x2-x1}[/tex] = [tex]\frac{1-0}{-2-(-2)}[/tex] = 1/0
=> This line does not have slope
