Question

Quick algebra 1 question for 50 points!

Answer 1

Answer:

b

Step-by-step explanation:

b shows direct variation because we can clearly tell that the slope of the graph is 1/2. The graph is also linear, and it crosses the origin (0,0).

a: This graph can be represented as y=2, and that is not a direct variation.

b: Above explanation. This graph is a direct variation.

c: This graph can be represented as x=-8, and that is not a direct variation.

d: This graph has the slope, but it does not cross the origin, so it is not a direct variation.

Answer 2

Answer:

Graph b

Step-by-step explanation:

Direct variation means "y varies directly as x”:

Direct variation equation:

$y=kx$

where k is the (non-zero) constant of variation.

Note, therefore, that a direct variation equation passes through the origin,  as when x = 0:  

$\implies y=k(0) \implies y=0$

Graph a

y does not change as x varies.

Therefore this graph does not model a direct variation.

Graph b

As x gets bigger, so does y.  As x gets smaller, so does y.  

The line passes through the origin (0, 0).

Therefore this graph models a direct variation.

Graph c

x does not change as y varies.

Therefore this graph does not model a direct variation.

Graph d

As x gets bigger, so does y.  As x gets smaller, so does y.  

However, the line does not pass through the origin (0, 0).

Therefore this graph does not model a direct variation.