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What are the Conditions for parallelism and perpendicularity of linear functions?
Condition of Parallelism: The Slope of two (lines) linear functions must be equal. i.e. m1=m2 Condition of perpendicularity : The product of slope of two (lines) linear functions must be equal to - 1. i.e. m1.m2=-1
What is the parent function of the linear function?
The parent function of a linear function is ( f(x) = x ). This function represents a straight line with a slope of 1 that passes through the origin (0,0). Linear functions can be expressed in the form ( f(x) = mx + b ), where ( m ) is the slope and ( b ) is the y-intercept, but all linear functions are transformations of the parent function ( f(x) = x ).
What is the point on the line where the slope changes?
The point on a line where the slope changes is typically referred to as a "corner" or "turning point," often found in piecewise functions or curves rather than linear functions. In these cases, the slope before and after this point differs, indicating a change in direction or steepness. For curves, this point might also be identified as a local maximum, minimum, or inflection point depending on the context. In linear functions, however, the slope remains constant throughout.
Why do all linear equations that descrbe functions written in point slope form?
Linear equations in point-slope form describe functions because they express the relationship between two variables (usually x and y) in a way that defines a straight line. The point-slope form, given by (y - y_1 = m(x - x_1)), emphasizes a specific point ((x_1, y_1)) on the line and the slope (m), which determines the line's steepness and direction. This format allows for easy identification of a line's characteristics, making it a useful representation for linear functions.
Do Linear functions have a vertex?
Linear functions do not have a vertex because they are represented by straight lines and lack curvature. A vertex is a feature of quadratic functions or other non-linear graphs where the direction of the curve changes. Linear functions are defined by the equation (y = mx + b), where (m) is the slope and (b) is the y-intercept, resulting in a constant rate of change without any turning points.
What are the Conditions for parallelism and perpendicularity of linear functions?
Condition of Parallelism: The Slope of two (lines) linear functions must be equal. i.e. m1=m2 Condition of perpendicularity : The product of slope of two (lines) linear functions must be equal to - 1. i.e. m1.m2=-1
Do linear function have a defined slope?
Not all linear functions have defined slope. In two dimension it is definet but in three dimensions it cant be defined; For that direction ratios are defined in mathematics.
Why do linear functions have a rate of change?
Linear functions have a rate of change because their slope parameter is non-zero. That is, as their x or y values changes, their corresponding x or y values change in response.
What is the parent function of the linear function?
The parent function of a linear function is ( f(x) = x ). This function represents a straight line with a slope of 1 that passes through the origin (0,0). Linear functions can be expressed in the form ( f(x) = mx + b ), where ( m ) is the slope and ( b ) is the y-intercept, but all linear functions are transformations of the parent function ( f(x) = x ).
Why can all linear equations that describe functions be written in point slope form?
Because a linear equation is, by definition, a straight line. Any line can be defined by selecting any one point on the line and the slope of the line.
What is the point on the line where the slope changes?
The point on a line where the slope changes is typically referred to as a "corner" or "turning point," often found in piecewise functions or curves rather than linear functions. In these cases, the slope before and after this point differs, indicating a change in direction or steepness. For curves, this point might also be identified as a local maximum, minimum, or inflection point depending on the context. In linear functions, however, the slope remains constant throughout.
Why do all linear equations that descrbe functions written in point slope form?
Linear equations in point-slope form describe functions because they express the relationship between two variables (usually x and y) in a way that defines a straight line. The point-slope form, given by (y - y_1 = m(x - x_1)), emphasizes a specific point ((x_1, y_1)) on the line and the slope (m), which determines the line's steepness and direction. This format allows for easy identification of a line's characteristics, making it a useful representation for linear functions.
Do Linear functions have a vertex?
Linear functions do not have a vertex because they are represented by straight lines and lack curvature. A vertex is a feature of quadratic functions or other non-linear graphs where the direction of the curve changes. Linear functions are defined by the equation (y = mx + b), where (m) is the slope and (b) is the y-intercept, resulting in a constant rate of change without any turning points.
Can the graph of a linear functions have undefined slope?
Yes. For example, the lines x=7, x=-1, and x=145 all have an undefined slope; they are all vertical.
A word for a constant rate of change?
In mathematics, a constant rate of change is called a slope. For linear functions, the slope would describe the curve of the function. The world "constant" in this context means the slope and therefore angle of the curve will not change.
What is the slope intercet form?
The slope-intercept form of a linear equation is expressed as ( y = mx + b ), where ( m ) represents the slope of the line and ( b ) is the y-intercept, the point where the line crosses the y-axis. This format makes it easy to identify both the slope and the y-intercept directly from the equation. It is widely used in algebra for graphing linear functions.
Does in linear graphs the slope of the line change with the x-coordinate?
No. A linear graph has the same slope anywhere.
