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Answer :
Let's analyze the given equation [tex]\( y = -x - 2 \)[/tex] to determine which statement is true.
1. Identify the form of the equation:
The equation [tex]\( y = -x - 2 \)[/tex] is in the form of [tex]\( y = mx + b \)[/tex]. This is known as the slope-intercept form of a linear equation, where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
2. Identify the slope and y-intercept:
From the equation [tex]\( y = -x - 2 \)[/tex]:
- The slope [tex]\( m \)[/tex] is [tex]\(-1\)[/tex].
- The y-intercept [tex]\( b \)[/tex] is [tex]\(-2\)[/tex].
3. Characteristics of linear equations:
- Linear equations produce graphs that are straight lines on a coordinate plane.
- The slope [tex]\( m = -1 \)[/tex] indicates that the line slopes downward from left to right.
4. Conclusion:
Since the equation is in the form of [tex]\( y = mx + b \)[/tex] and represents a straight line when graphed, it is a linear equation.
Thus, the correct statement is:
- The equation represents a linear function because when graphed on a coordinate plane, the graph will be a straight line.
1. Identify the form of the equation:
The equation [tex]\( y = -x - 2 \)[/tex] is in the form of [tex]\( y = mx + b \)[/tex]. This is known as the slope-intercept form of a linear equation, where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
2. Identify the slope and y-intercept:
From the equation [tex]\( y = -x - 2 \)[/tex]:
- The slope [tex]\( m \)[/tex] is [tex]\(-1\)[/tex].
- The y-intercept [tex]\( b \)[/tex] is [tex]\(-2\)[/tex].
3. Characteristics of linear equations:
- Linear equations produce graphs that are straight lines on a coordinate plane.
- The slope [tex]\( m = -1 \)[/tex] indicates that the line slopes downward from left to right.
4. Conclusion:
Since the equation is in the form of [tex]\( y = mx + b \)[/tex] and represents a straight line when graphed, it is a linear equation.
Thus, the correct statement is:
- The equation represents a linear function because when graphed on a coordinate plane, the graph will be a straight line.
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