Question

Analyzing a Linear Function Expressed in Different Ways
A linear function is expressed by a graph of a line that crosses both axes at the origin. An equation is written in slope-intercept form to express the same function as shown in the graph. From just this information, what statements can be made?

Choose the true statements.
The slope of the equation must be positive.
The y-intercept of the equation is zero.
It is possible that the line on the graph is horizontal.
The slope of the equation must be negative.

Answer 1

True:
- The y-intercept of the equation is zero. (If the line passes through the origin, in y = mx + b we have b = 0.)
- It is possible that the line on the graph is horizontal. (That would be y = 0, i.e. m = 0.)

False:
- The slope must be positive. (The slope can be positive, negative, or zero.)
- The slope must be negative. (Not required.)