Question

For the line 9x−3y=−18, what statement is true?

A) The line has a positive slope.

B) The line has a negative slope.

C) The line is vertical.

D) The line is horizontal.

Answer 1

The equation 9x-3y=-18 represents a line with a positive slope once it is rewritten in slope-intercept form, which is y = 3x + 6, indicating that the slope (m) is positive 3.

Step-by-step explanation:

For the line given by the equation 9x−3y=−18, we can determine the slope by rewriting it in slope-intercept form (y = mx + b), where m represents the slope and b the y-intercept. First, we add 3y to both sides and then subtract 18 from both sides to isolate y, yielding:

3y = 9x + 18

Now, divide every term by 3:

y = 3x + 6

This shows that the slope (m) is 3, which is a positive number. Therefore, the line has a positive slope.

Option A is correct because a positive slope means that as x increases, y also increases, corresponding to an upward slope from left to right on the graph.