Video transcript
Write an inequality that fits the graph shown below. So here they've graphed a line in red, and the inequality includes this line because it's in bold red. It's not a dashed line. It's going to be all of the area above it. So it's all the area y is going to be greater than or equal to this line. So first we just have to figure out the equation of this line. We can figure out its y-intercept just by looking at it. Its y-intercept is right there. Let me do that in a darker color. Its y-intercept is right there at y is equal to negative 2. That's the point 0, negative 2. So if you think about this line, if you think about its equation as being of the form y is equal to mx plus b in slope-intercept form, we figured out b is equal to negative 2. So that is negative 2 right there. And let's think about its slope. If we move 2 in the x-direction, if delta x is equal to 2, if our change in x is positive 2, what is our change in y? Our change in y is equal to negative 1. Slope, or this m, is equal to change in y over change in x, which is equal to, in this case, negative 1 over 2, or negative 1/2. And just to reinforce, you could have done this anywhere. You could have said, hey, what happens if I go back 4 in x? So if I went back 4, if delta x was negative 4, if delta x is equal to negative 4, then delta y is equal to positive 2. And once again, delta y over delta x would be positive 2 over negative 4, which is also negative 1/2. I just want to reinforce that it's not dependent on how far I move along in x or whether I go forward or backward. You're always going to get or you should always get, the same slope. It's negative 1/2. So the equation of that line is y is equal to the slope, negative 1/2x, plus the y-intercept, minus 2. That's the equation of this line right there. Now, this inequality includes that line and everything above it for any x value. Let's say x is equal to 1. This line will tell us-- well, let's take this point so we get to an integer. Let's say that x is equal to 2. Let me get rid of that 1. When x is equal to 2, this value is going to give us negative 1/2 times 2, which is negative 1, minus 2, is going to give us negative 3. But this inequality isn't just y is equal to negative 3. y would be negative 3 or all of the values greater than negative 3. I know that, because they shaded in this whole area up here. So the equation, or, as I should say, the inequality that fits the graph here below is-- and I'll do it in a bold color-- is y is greater than or equal to negative 1/2x minus 2. That is the inequality that is depicted in this graph, where this is just the line, but we want all of the area above and equal to the line. So that's what we have for the inequality.
Chapter 4 Student Learning Objectives
SLO 4.1 - I can Interpret the slope and y-intercept in context.
SLO 4.2 - I can make a prediction by evaluating the equation of a line of best fit.
SLO 4.3 - I can use a
calculator to calculate and interpret LSRL, residuals, correlation coefficient (r) and r^2.
SLO 4.4 - I can write equations for upper and lower bounds, and use them to create a range of predictions.
Extra Practice:
- PDF Lesson 4.1.1: Line of Best Fit
- PDF Lesson 4.1.2 & 4.1.3: Residuals and Upper and Lower Bounds
- PDF Lesson 4.1.4: Least Squares Regression Line
- PDF Lesson 4.2.1, 4.2.2, & 4.2.4: Residual Plots and Correlation
- PDF Lesson 4.2.3: Association and Causation
5.4.4 Practice:Modeling: Two-Variable Systems of InequalitiesPracticeAlgebra I Sem 1Points Possible:20Name:Aryan ChatterjeeDate:In this assignment, you may work alone, with a partner, or in a small group. Discuss theresults of your work and/or any lingering questions with your teacher.Your Assignment: Parks and Recreation Workshop PlanningYou are helping with the planning of workshops offered by your city's Parks andRecreation department. The director of programs has asked you to purchase snacks forone of the two workshops currently scheduled. Circle the workshop you picked:What do you know?I know that I have a budget of $40 for the watercolor workshop and a budget of $48 forthe baseball clinic. I want to buy fruits, which cost $4 per pound, and granola bars,which cost $1 each. I need at least 20 for the watercolor workshop and 10 for thebaseball clinic.What do you want to find out?I want to find out what combinations of fruit and granola bars I can buy for bothworkshops.