Question

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

Which statement about the slope of the line is true?
It is –2 throughout the line.
It is fraction negative 1 over 2 throughout the line.
The slope from point O to point A is one-half times the slope of the line from point A to point B. The slope from point O to point A is two times the slope of the line from point A to point B.

Answer 1

Every time the y-value decreases by 1, the x-value increases by 2, so the slope is -1/2 throughout the line.

Answer 2

The slope is fraction negative 1 over 2 throughout the line.

Explanation:

The slope (m) of a line is computed as follows

m = (y2 - y1)/(x2 -x1)

where (x1, y1) and (x2, y2) are the coordinates of 2 points of the line. Taking, for example, points (0, 0) and (-4, 2), the slope is:

m = (2 - 0)/(-4 -0) = -1/2

Then, the slope is -1/2 throughout the line.