#LINEAR FUNCTION GRAPH PLUS#

So he was connecting the slope back to the incremental change in cost, which was a really nice connection. He asked students to look for any pattern they saw in the table and they could see that there was a 24-cent difference between each of the y-values in the table. When the students were talking about the slope and they said that 24 cents was the slope, he didn’t stop there. See what Diane Briars has to say about the important aspects of linear functions that Tom Reardon applied in his lesson: They discussed the meaning of the constants in the equation and how those constants affected both the table and the graph. The students then produced an equation and a graph to further describe the situation. For example, in the video for Workshop 2, Part I, Tom Reardon started with a verbal description and a table of values. To do this, they need ample opportunity to explore situations involving linear functions in all representations. Likewise, when given one representation of a linear function, students should be able to produce the others. Students should be able to move fluently between the different representations of linear functions and, given a description of a situation, should be able to produce a table, equation, and graph. (NCTM, Principles and Standards for School Mathematics,

The linear function I = 400C + 1,500 yields the total monthly income of a car salesman who makes a monthly base salary of $1,500 and receives $400 dollars for each car sold.

If the fixed rate is $25, and the cost for each unit of power is $0.02, the linear function is C = 0.02P + 25.

#LINEAR FUNCTION GRAPH PLUS#

If a utility company charges a fixed monthly rate plus a constant rate for each unit of power consumed, a linear function will show the monthly cost of power.

The linear function F = 1.8C + 32 can be used to convert temperatures between Celsius and Fahrenheit.

Through practical experience solving linear function problems in context, students will develop an understanding of the concepts and real-world meanings of the slopes and y-intercepts of lines.

When studying linear functions graphically, students should understand that the slope of the line represents a constant rate of change for the function, and that the y-intercept is the point where the graph crosses the y-axis and often represents the initial condition or starting point for the function. Students should be able to recognize a linear function in a table of values, a graph, or in algebraic form. Each form provides different information about the function.

Linear functions can be written in three different forms, as shown in the table below. Students should solve problems in which they use tables, graphs, words, and symbolic expressions to represent and examine linear functions and linear patterns of change. Linear functions arise when there is a constant rate of change. Linear functions model a wide variety of real-world situations, including predicting the cost of a telephone call that lasts a given amount of time, the profit of a hot dog stand, and the amount of tax paid for a given income.

Linear function graph