Answer :
To determine whether the given statement is true or false, let's break down the components of the equation of a line in slope-intercept form, which is [tex]\( y = mx + b \)[/tex].
Step 1: Identify the standard form of the slope-intercept equation.
The equation [tex]\( y = mx + b \)[/tex] is known as the slope-intercept form of a linear equation. In this form:
- [tex]\( y \)[/tex] represents the dependent variable (usually the output or vertical coordinate on a graph).
- [tex]\( x \)[/tex] represents the independent variable (usually the input or horizontal coordinate on a graph).
- [tex]\( m \)[/tex] represents the slope of the line. The slope measures the steepness of the line and is calculated as the ratio of the vertical change ([tex]\( \Delta y \)[/tex]) to the horizontal change ([tex]\( \Delta x \)[/tex]) between two points on the line.
- [tex]\( b \)[/tex] represents the y-intercept of the line. The y-intercept is the point where the line crosses the y-axis (i.e., when [tex]\( x = 0 \)[/tex]).
Step 2: Validate the components.
- The term [tex]\( m \)[/tex] correctly identifies the slope of the line. This is the coefficient of [tex]\( x \)[/tex], indicating how much [tex]\( y \)[/tex] changes for a given change in [tex]\( x \)[/tex].
- The term [tex]\( b \)[/tex] correctly represents the y-intercept, which is the value of [tex]\( y \)[/tex] when [tex]\( x = 0 \)[/tex].
Based on these components and their definitions, the equation [tex]\( y = mx + b \)[/tex] precisely describes a line in the slope-intercept form.
Conclusion:
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 accurate.
Therefore, the correct answer is:
A. True
Step 1: Identify the standard form of the slope-intercept equation.
The equation [tex]\( y = mx + b \)[/tex] is known as the slope-intercept form of a linear equation. In this form:
- [tex]\( y \)[/tex] represents the dependent variable (usually the output or vertical coordinate on a graph).
- [tex]\( x \)[/tex] represents the independent variable (usually the input or horizontal coordinate on a graph).
- [tex]\( m \)[/tex] represents the slope of the line. The slope measures the steepness of the line and is calculated as the ratio of the vertical change ([tex]\( \Delta y \)[/tex]) to the horizontal change ([tex]\( \Delta x \)[/tex]) between two points on the line.
- [tex]\( b \)[/tex] represents the y-intercept of the line. The y-intercept is the point where the line crosses the y-axis (i.e., when [tex]\( x = 0 \)[/tex]).
Step 2: Validate the components.
- The term [tex]\( m \)[/tex] correctly identifies the slope of the line. This is the coefficient of [tex]\( x \)[/tex], indicating how much [tex]\( y \)[/tex] changes for a given change in [tex]\( x \)[/tex].
- The term [tex]\( b \)[/tex] correctly represents the y-intercept, which is the value of [tex]\( y \)[/tex] when [tex]\( x = 0 \)[/tex].
Based on these components and their definitions, the equation [tex]\( y = mx + b \)[/tex] precisely describes a line in the slope-intercept form.
Conclusion:
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 accurate.
Therefore, the correct answer is:
A. True
