Let's solve this problem step-by-step.
The question asks whether the equation of a line in slope-intercept form is [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope of the line.
1. Understanding Slope-Intercept Form:
In mathematics, the slope-intercept form of the equation of a line is typically written as [tex]\( y = mx + b \)[/tex].
- Here, [tex]\( y \)[/tex] represents the [tex]\( y \)[/tex]-coordinate of any point on the line.
- [tex]\( x \)[/tex] represents the [tex]\( x \)[/tex]-coordinate of any point on the line.
- [tex]\( m \)[/tex] is the slope of the line, which indicates how steep the line is.
- [tex]\( b \)[/tex] is the y-intercept, which is the point where the line intersects the y-axis (i.e., where [tex]\( x = 0 \)[/tex]).
2. Interpreting the Components:
- The slope [tex]\( m \)[/tex] shows the rate of change of [tex]\( y \)[/tex] with respect to [tex]\( x \)[/tex]. A larger [tex]\( m \)[/tex] value means a steeper incline if [tex]\( m \)[/tex] is positive, or a steeper decline if [tex]\( m \)[/tex] is negative.
- The y-intercept [tex]\( b \)[/tex] is simply the value of [tex]\( y \)[/tex] when [tex]\( x \)[/tex] is 0. It locates the line vertically on the graph.
3. Validating the Statement:
Given the equation [tex]\( y = mx + b \)[/tex]:
- The form matches the given description with [tex]\( m \)[/tex] as the slope.
- This setup aligns correctly with the understanding from algebra about the structure of linear equations.
Therefore, the statement "The equation of a line in slope-intercept form is [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope of the line." is indeed correct.
Thus, the correct answer is:
A. True
