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

A line is shown on a coordinate grid. The x axis values are from negative 20 to positive 20 in increments of 4 for each grid line. The y axis values are from negative 5 to positive 5 in increments of 1 for each grid line. The line passes through the ordered pairs negative 16, negative 4, and 0, 0, and 16, 4. A shaded right triangle is formed so that its hypotenuse is from ordered pair 0, 0 labeled as O to negative 8, negative 2 labeled as A, one leg is from 0, 0 to 0, negative 2, and the second leg is from 0, negative 2 to negative 8, negative 2. Another shaded right triangle is formed with the hypotenuse from negative 8, negative 2 to negative 12, negative 3 labeled as B, one leg is from negative 8, negative 2 to negative 8, negative 3, and the second leg is from negative 12, negative 3 to negative 8, negative 3.

Which statement about the slope of the line is true?

The slope from point O to point A is fraction 1 over 4 time 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
It is 4 throughout the line.
It is fraction 1 over 4 throughout the line.

Answer:

The answer is D

Step-by-step explanation:

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The slope is 4 throughout the line.

Option C is the correct answer.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

Two coordinates between O and A.

((0, 0) and (-1, -4)

The slope of the line from O to A.

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

= -4/-1

= 4 _____(1)

Two coordinates between A and B.

(-2, -8) and (-3, -12)

The slope of the line from A to B.

= (-12 + 8) / (-3 + 2)

= -4/-1

= 4 _______(2)

From (1) and (2) we get,

The slope is 4 throughout the line.

Thus,

The slope is 4 throughout the line.

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