Lesson 4: 3-4 Slope-Intercept Form (converting)
Duration of Days: 5
Lesson Objective
Write and graph linear equations in slope-intercept form.
Model real-world data with equations in slope-intercept form.
Which variable represents slope in the slope-intercept form?
Which variable repreents the y-intercept in the slope-intercept form?
If you know the location of one point on a line and that the slope of the line is -3, how can you locate another point on the line?
A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
F.IF.7a Graph linear and quadratic functions and show intercepts, maxima, and minima.
SAT questions related to slope: 8-3-13,6-3-1,5-4-7,8-3-19,7-4-17,1-3-6,3-4-8;
graphing: 6-3-5;
functions: 3-4-4, 5-4-2, 6-4-25
An equation written in slope-intercept form can be graphed in two different ways. The first way is to select two values of x, and substitute those values into the equation. Then calculate the corresponding values of y to create two ordered pairs that can be graphed. The second way is to graph the y-intercept, and use the slope to determine the distance and direction to move to find another point on the line.
Jamil has 500 songs on his smartphone. He joins a music club that lets him download 30 songs per month for a monthly fee. the number of songs that Jamil could eventually have if he does not delete any songs is represented by y = 30x + 500 for x months.
Preventing Errors Remind students that b can be negative, so equations may not always have positive constraints.
If some students have difficulty with word problems because they cannot picture what the problem is trying to communicate, then sometimes it is easier for those students to graph or draw a picture of the given information before writing the equation. For Guided Practice 5, you may wish to have students do part b first by using the starting point and the rate of change to determine other points on the graph. Then have students write the equation that describes the line formed.
Extension Write 3x + 2y = 8 and -3x + 2y = 8 on the board. Remind students that these equations are in the standard form for the equation of a line. Ask students to tell how the equations are alike and how they are different. Then, ask students to tell how the graphs of these two equations are alike and how they are different.
Exercises 67 - 74
Access textbook through Classlink