In the xy-plane, the slope of the line y = mx - 4 is less than the slope of the line y = x - 4. What must be true about m?
Understand the Problem
The question is asking for the condition that must be true about the slope 'm' of the line y = mx - 4, given that this slope is less than the slope of the line y = x - 4. This involves understanding the relationship between the slopes of linear equations.
Answer
The condition is $m < 1$.
Answer for screen readers
The condition that must be true about $m$ is $m < 1$.
Steps to Solve
-
Identify the slopes of the equations
The slope of the line $y = mx - 4$ is $m$.
The slope of the line $y = x - 4$ is $1$. -
Set up the inequality
Since the problem states that the slope of the first line is less than the slope of the second line, we can write the inequality as:
$$ m < 1 $$ -
Interpret the result
This means that for the line $y = mx - 4$ to have a slope less than that of the line $y = x - 4$, the value of $m$ must be any number that is less than $1$.
The condition that must be true about $m$ is $m < 1$.
More Information
This inequality indicates that the slope of the line $y = mx - 4$ is decreasing as compared to the slope of the line $y = x - 4$. A slope of less than 1 suggests a less steep line in the positive direction.
Tips
null
AI-generated content may contain errors. Please verify critical information
