Question

Which statement best explains the relationship between

Answer 1

Answer:

The best statement which explains the relationship between lines AB and CD is "They are parallel because their slopes are equal" ⇒ A

Step-by-step explanation:

• Parallel lines have equal slopes and different y-intercepts

• The rule of the slope of a line passes through points (x1, y1) and (x2, y2) is m = $\frac{y2-y1}{x2-x1}$

In the given figure

∵ The blue line passes through points A and B

∵ A = (-4, -2) and B = (4, 4)

∴ x1 = -4 and y1 = -2

∴ x2 = 4 and y2 = 4

→ Substitute them in the rule of the slope

∵ m(AB) = $\frac{4--2}{4--4}$ = $\frac{4+2}{4+4}$ = $\frac{6}{8}$ = $\frac{3}{4}$

∴ The slope of line AB is  $\frac{3}{4}$

∵ The green line passes through points C and D

∵ C = (0, -3) and D = (4, 0)

∴ x1 = 0 and y1 = -3

∴ x2 = 4 and y2 = 0

→ Substitute them in the rule of the slope

∵ m(CD) = $\frac{0--3}{4-0}$ = $\frac{0+3}{4}$ = $\frac{3}{4}$

∴ The slope of line CD is  $\frac{3}{4}$

∵ The slope of line AB = the slope of line CD

∵ Parallel lines have the same slope

∴ AB // CD

∴ AB and CD are parallel lines

The best statement which explains the relationship between lines AB and CD is "They are parallel because their slopes are equal"