Jeffrey Coolidge/The Image Bank/Getty Images Updated on October 18, 2019 Each type of algebra function is its own family and possesses unique traits. If you want to understand the characteristics of each
family, study its parent function, a template of domain and range that extends to other members of the family. The most basic parent function is the linear parent function. In the phrase "algebra functions," a function
is a set of data that has one distinct output (y) for each input (x). A function also describes the relationship between inputs (x) and outputs (y). As a testament to the various patterns between x and y, several types of functions exist: In algebra, a linear equation is one that contains two variables and can be plotted on a graph as a straight line. Key common points of linear parent functions include the fact that the: You can see the physical representation of a linear parent function on a
graph of y = x. Family members have common and contrasting attributes. If your dad has a big nose, for example, then you probably have one as well. Nonetheless,
just as you are different from your parents, so is a subsequent function different from its parent. For the linear parent functions below, note that any changes to the equation will alter the graph. Vertical shifts: y = x+1 The graph shifts up 1 unit. y= x-4 The graph shifts down 4 units. Changes in steepness: y= 3x The graph becomes steeper. y = ½x The graph becomes flatter. Negative influence: y = The graph flips and slopes downward, instead of upward. (This is also called a negative slope.) The steepness of a hill is called a slope. The same goes for the steepness of a line. The slope is defined as the ratio of the vertical change between two points, the rise, to the horizontal change between the same two points, the run. $$slope=\frac{rise}{run}=\frac{change\: in \: y}{change \: in\: x}$$  The slope of a line is usually represented by the letter m. (x1, y1) represents the first point whereas (x2, y2) represents the second point. $$m=\frac{y_{2}\, -y_{1}}{x_{2}\, -x_{1}}$$ It is important to keep the x-and y-coordinates in the same order in both the numerator and the denominator otherwise you will get the wrong slope. Example Find the slope of the line (x1, y1) = (-3, -2) and (x2, y2) = (2, 2) $$m=\frac{y_{2}\, -y_{1}}{x_{2}\, -x_{1}}=\frac{2-\left ( -2 \right )}{2-\left ( -3 \right )}=\frac{2+2}{2+3}=\frac{4}{5}$$ A line with a positive slope (m > 0), as the line above, rises from left to right whereas a line with a negative slope (m < 0) falls from left to right. $$m=\frac{y_{2}\, -y_{1}}{x_{2}\, -x_{1}}=\frac{\left (-1 \right )-3}{2-\left ( -2 \right )}=\frac{-1-3}{2+2}=\frac{-4}{4}=-1$$ If two lines have the same slope the lines are said to be parallel. You can express a linear function using the slope intercept form. $$y=mx+b$$ $$m=slope$$ $$b=y - intercept$$ Video lessonFind the slope Does a linear parent function have a slope of 0?Answer and Explanation: Yes, a linear function can have a slope of zero. In fact, all horizontal lines, or lines with the function y = b, where b is any constant, have a slope of zero. The points of a horizontal line, y = b, all have the same y-value of b.
Does a linear function have a slope?With positive slope the line moves upward when going from left to right. With negative slope the line moves down when going from left to right. If two linear functions have the same slope they are parallel. The slope of a linear function is the same no matter where on the line it is measured.
What is a parent function for a linear function?Linear Parent Function: The most basic function in a family. For linear functions, the parent function is y = x or f(x) = x. Transformation: A change in position or size of a figure.
Are linear functions 1 1?From this, we can conclude that all linear functions are one-to-one functions.
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Does a linear parent function have a slope of 1
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