Refer to the above diagram.The slope of the line: A)is -¹/₄. B)is +¹/₄. C)is .40. D)cannot be determined from the information given.

Question

Quizplus · Accepted Answer

The slope of a line is rise (change in y-coordinate) over run (change in x-coordinate). From the diagram, we can see that the rise is S1S1P0 and the run is S1U1B0. Therefore, the slope is S1S1P0/S1U1B0. To find this ratio, we need to break it down into smaller segments: S1S1P0 = S1S1P11 + P11P0 and S1U1B0 = S1U1B14 + B14B0. We can see from the diagram that S1S1P11 = -S1U1P11 and P11P0 = -S1P0. Similarly, S1U1B14 = -B14U1S1 and B14B0 = -U1B0. Substituting these values, we get:

S1S1P0/S1U1B0 = (S1S1P11 + P11P0)/(S1U1B14 + B14B0)
= (-S1U1P11 - S1P0)/(-B14U1S1 - U1B0)
= (S1U1P11 + S1P0)/(B14U1S1 + U1B0)
= S1U1P11S1S1P0/S1U1B14S1U1B0

Therefore, the slope of the line is S1U1P11S1S1P0/S1U1B14S1U1B0, which is positive (since the numerator and denominator are both negative). This matches option B.

Refer to the Above Diagram