6. if two quantities vary directly, which must be true of a graph showing the relationship between them?
a. the graph is a curve.
b. the graph increases from left to right.
c. the points on the graph are connected.
d. the points of the graph form a straight line, and the line must pass through the origin.

The points of the graph form a straight line, and the line must pass

through the origin ⇒ answer d

Step-by-step explanation:

* Lets explain the meaning of vary directly

- Direct variation is a relationship between two variables

- Two variable quantities have a constant ratio

- One of them equal the other multiplied by a constant

- If y varies directly with x, the y = kx, where k is the constant

 of variation

- The equation y = kx is represented graphically by a line

- If the value of x = 0 then the value of y must be equal zero, then the

 line which represented the direct variation must be passes through

  the origin

* Lets look to the answer to find the correct statement

a. The graph is a curve ⇒ Not true ⇒The graph must be line

b. The graph increases from left to right ⇒ Not true ⇒ maybe if the

    graph is a line there is no mention about the type of the graph

c. The points on the graph are connected ⇒ Not true ⇒ there is no

    mention about the type of the graph

d. The points of the graph form a straight line, and the line must pass

    through the origin ⇒ True ⇒ as we said above

* The answer is statement d

the transverse axis of a hyperbola is the line that contains the two vertices and the two focuses.

in this example (hyperbola of equation x^2/2 - y^2/4 = 1), the transverse axis is the  x-axis  . 

step-by-step explanation: