Question

Whcih of the following proportional orders has a graph with a slope different from the others?
A. a proportional linear equations that contains the point (-2,-5)
B. a proportional linear equations that contains the point (20,8)
C.a proportional linear equations that contains the point (-1,-2.5)
D. a proportional linear equations that contains the point (4,10)

Answer 1

In order to determine which proportional linear equation has a slope different from the others, we first need to calculate the slope for each equation using the form of proportional relationships, which is \(y = kx\), where \(k\) is the constant of proportionality (slope).

The slope can be calculated as \(\frac{y}{x}\) for each point:

A. For the point (-2, -5):
\[
\text{slope} = \frac{-5}{-2} = \frac{5}{2} = 2.5
\]

B. For the point (20, 8):
\[
\text{slope} = \frac{8}{20} = \frac{2}{5} = 0.4
\]

C. For the point (-1, -2.5):
\[
\text{slope} = \frac{-2.5}{-1} = 2.5
\]

D. For the point (4, 10):
\[
\text{slope} = \frac{10}{4} = \frac{5}{2} = 2.5
\]

Now, summarizing the slopes:
- A: 2.5
- B: 0.4
- C: 2.5
- D: 2.5

From this, we can see that the slope for option B (0.4) is different from the others. Thus, the answer is:

**B. a proportional linear equation that contains the point (20, 8)**.