Question

question 1 of 10
the equation ( y = ax ) describes the graph of a line. if the value of ( a ) is positive, the line:
a. is horizontal.
b. goes down and to the right.
c. goes up and to the right.
d. is vertical.

Explanation:

The equation \( y = ax \) is a linear equation in slope - intercept form (\( y=mx + b \), here \( b = 0\)) where \( a\) (or \( m\) in the general form) represents the slope of the line. The slope of a line describes the direction and the steepness of the line. If the slope (\( a\)) is positive, it means that as the value of \( x\) (the independent variable, moving to the right along the \( x\) - axis) increases, the value of \( y\) (the dependent variable) also increases. So, the line goes up (because \( y\) increases) and to the right (because \( x\) increases). A horizontal line has a slope of 0 (so option A is incorrect), a line that goes down and to the right has a negative slope (so option B is incorrect), and a vertical line has an undefined slope (not in the form \( y = ax\) with a defined \( a\), so option D is incorrect).

Answer:

C. goes up and to the right.