Question

Do the points (0.-9). (-3.-18) and (2,-3) lie on the same line? Explain why or why not. (Hint: Find the slopes between the points.)

Do the three points lie on the same line?
A. No, because the slopes are not the same.
B. Yes, because the slopes are the same. C. Yes, because the slopes are not the same.
D. No, because the slopes are the same.

Answer 1

B

Explanation:

if the points lie on the same line then the slope between consecutive points will be equal.

calculate the slope using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (0, - 9) and (x₂, y₂ ) = (- 3, - 18) ← first and second points

substitute these values into the formula for m

m =
`(-18-(-9))/(-3-0)` =
`(-18+9)/(-3)` =
`(-9)/(-3)` = 3

repeat with

(x₁, y₁ ) = (- 3, - 18) and (x₂, y₂ ) = (2, - 3) ← second and third points

m =
`(-3-(-18))/(2-(-3))` =
`(-3+18)/(2+3)` =
`(15)/(5)` = 3

the 3 points lie on the same line because the slopes are the same