Question

The figure below shows a line graph and two shaded triangles that are similar:

-20-16-12-8-40
-1
4 8 12 16 20
Which statement about the slope of the line is true?
The slope from point o to point A is one-fourth times the slope of the line from point A to point B.
The slope from point o to point A is four times the slope of the line from point A to point B.
Olt is throughout the line
It is -4 throughout the line.

Answer 1

It is -
`(1)/(4)` throughout the line

Explanation:

The points O, A and B lie on the line and so the slope will be the same for OA, OB and AB

Calculate the slope m using the slope formula

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

with (x₁, y₁ ) = B(- 12, 3) and (x₂, y₂ ) = O(0, 0)

m =
`(0-3)/(0+12)` =
`(-3)/(12)` = -
`(1)/(4)`

Thus the slope is -
`(1)/(4)` throughout the line.