Let's break down the components of the equation of a line in slope-intercept form, which is written as:
[tex]\[ y = mx + b \][/tex]
In this equation:
- [tex]\( y \)[/tex] represents the dependent variable (typically the vertical axis in a graph).
- [tex]\( x \)[/tex] represents the independent variable (typically the horizontal axis in a graph).
- [tex]\( m \)[/tex] represents the slope of the line.
- [tex]\( b \)[/tex] represents the y-intercept of the line (the value of [tex]\( y \)[/tex] when [tex]\( x \)[/tex] is 0).
To clarify further:
- The slope [tex]\( m \)[/tex] indicates how steep the line is. It is defined as the rise over the run or the change in [tex]\( y \)[/tex] divided by the change in [tex]\( x \)[/tex] between any two points on the line.
- The y-intercept [tex]\( b \)[/tex] is the point where the line crosses the y-axis. This is the value of [tex]\( y \)[/tex] when [tex]\( x \)[/tex] is zero.
Given the question at hand:
- The assertion is that in the equation [tex]\( y = mx + b \)[/tex], [tex]\( m \)[/tex] represents the [tex]\( x \)[/tex]-intercept.
This statement is incorrect. The correct interpretation is that [tex]\( m \)[/tex] is the slope of the line, not the [tex]\( x \)[/tex]-intercept.
Therefore, the correct answer is:
B. False
