Question

1. what are important graphical features of proportional relationships? circle all correct statements:

a. the graph is a straight line.
b. the line has a y-intercept of 0.
c. the line passes through the origin.
d. the line has an x-intercept of 0.
e. the line passes through the point (0,0).

Explanation:

A proportional relationship is of the form \( y = kx \) (where \( k \) is the constant of proportionality).

• For option a: The graph of \( y = kx \) is a straight line (linear), so this is correct.
• For option b: The y - intercept is found by setting \( x = 0 \), then \( y=k(0) = 0 \), so the y - intercept is 0, correct.
• For option c: The origin is \( (0,0) \), and when \( x = 0 \), \( y = 0 \), so the line passes through the origin, correct.
• For option d: The x - intercept is found by setting \( y = 0 \), then \( 0=kx\Rightarrow x = 0 \) (since \( k

eq0 \) for a proportional relationship), so the x - intercept is 0, correct.

• For option e: The point \( (0,0) \) is the origin, and as shown above, the line \( y = kx \) passes through \( (0,0) \), correct.

Answer:

a. The graph is a straight line, b. The line has a y - intercept of 0, c. The line passes through the origin, d. The line has an x - intercept of 0, e. The line passes through the point (0,0)