Published on March 17, 2018
Represent and Solve Equations and Inequalities Graphically. : Represent and Solve E quations and Inequalities G raphically . Nicolas Caulfield EDSC 304 Looking Back at Polynomials: Looking Back at Polynomials How do you solve a single variable equation? By isolating the variable to solve and to make sure that the coefficients are out of the variable. What you do to one side you have to do the other. You can use multiplication, division, addition, or subtraction to get to the answer. Ex: Solve 13 – 2x = 8x + 3 Inequalities: Inequalities How similar are these to regular polynomials? Very similar, you use the same methods to solve these but with small rules. If you are multiplying or dividing by a negative number the inequality sign has to be flipped. Ex: -4y + 5 > 2y -7 A look at graphing: A look at graphing How does this tie in? With graphing, the variables are going to be plotted onto an x and y graph, which in other terms is the coordinate plane. It is composed of the x and y axis respectively as well as the origin is the center point within the graph as shown with the red line. Graphing Example: Graphing Example Ex: x = 1 (red), y = 1 (blue) A tip for remembering is that they act as opposites to the axis they’re named after. This graph was made in Desmos a free graphing calculator online that I highly recommend using. Graphing Continued: Graphing Continued With graphing a linear model, graphs use a standard form to map out the equation y = mx + b is the standard form for graphing po lynomials X and Y are still part of the graph and coordinates but with an added m for the slope of the line as well as b for the y – intercept of the line, where the x – coordinate equals zero so y is on the y – axis. Slope Intercept Graphing Example: Slope Intercept Graphing Example Ex: Graph y = 2x + 1 and y = 4x As you can see, these graphs intercept at a certain point. You can find that point by setting the two equations equal to each other and solve for the variables like any other polynomial. By setting them equal to each other, you will get both the x and y coordinate for the graphs. Inequalities and Graphing: Inequalities and Graphing How do you show the inequality of an equation? We treat this like a regular polynomial as if the inequality is an equal sign FOR THE INITIAL SETUP! We do this to see what we’re working with and to approach it in an easier way. The main difference is displaying the values in which the inequality falls in For example: y > 2x +4 can be graphed as y = 2x + 4 Graphing Inequalities Khan Academy: Graphing Inequalities Khan Academy Graphing Two Variable Inequalities – Khan Academy This video gives a good explanation to how to approach an inequality graph from the site Khan Academy Looking back at Word Problems: Looking back at Word Problems Quick Review of Word Problems How do you approach one? What does the description mean? Word problems can be tricky because of the wording is framed in a evasive way from the problems. Ex: If Becky makes $6 for every burger and $3 for every order of fries she sells, how many does she need to sell in order to break even of her original amount of $100? How many of each does she need to sell in order to make $250? Working out Word Problems: Working out Word Problems What is our equation? Is that amount reasonable? Word problems add an element of realism to the problem having to do with real world problems, if you have a negative amount of money in order to make a profit, then something isn’t quite right. Connecting the real world and math is essential to problem solving and critical thinking in other classes as well as future math classes.