130 Chapter 3 Writing Linear Equations and Linear Systems 1. The formula for linear equation is y=mx+b. A linear function describes a gradual rate of change, either positive or negative. What does the y-intercept represent in your example? Real world uses for linear functions include solving problems and finding unknowns in engineering, economics and finances. REASONING In a real-life situation, what does the slope of a line represent? Solving quadratic equations by factoring. As one of the tools of mathematics, linear systems have multiple uses in the real world. Sum and product of the roots of a quadratic equations Algebraic identities One application of linear equations is illustrated in finding the time it takes for two cars moving toward each other at different speeds to reach the same point. Linear equations can be used to model many types of real life situation word problems, such as cost, profit, speed, distance and time problems. b) Find the slope of the graph and explain what information it gives about the situation. 3. Remember, when solving a system of linear equations, we are looking for points the two lines have in common. Real-life examples of linear equations include distance and rate problems, pricing problems, calculating dimensions and mixing different percentages of solutions. So much of the world runs by mathematical rules. Life is full of situations when the output of a system doubles if the input doubles, and the output cuts in half if the input does the same. Any linear system can be described with a linear equation. They are applicable in many real life cases. A well known real world math incident that almost cost a Verizon customer a large amount of money (Hint: there's a difference between .02 cents and .02 dollars!) Solving linear equations using cross multiplication method. After the model is written and a graph of the line is made, either one can be used to make predictions about behaviors. What does the slope represent in your example? A real life example of linear equations could be a car driving on the highway, and how much gas it uses in a trip. To solve the word problems, you need to interpret the situation described in the problem into an equation, then solve the problem by solving the equation. When drawn, it presents a straight line. The graph shows the linear growth of the saplings, in centimeters. Fortunately, statistical software makes it easy to perform linear regression. Real-world situations including two or more linear functions may be modeled with a system of linear equations. Feel free to explore the following tutorials to learn how to perform linear regression using different softwares: Get an answer to your question “A linear function that models a real-life situation is called a ...” in Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions. OPEN-ENDED Describe a real-life situation that uses a negative slope. Describe a real-life scenario in which you may have to graph (or use) a linear equation. A linear model includes the rate of change [latex](m)[/latex] and the initial amount, the y-intercept [latex]b[/latex]. The periodic rotations of a crankshaft in an engine; The rotation of a Ferris wheel Solving quadratic equations by quadratic formula. Lesson 4.5 Real-World Problems: Linear Equations Solve. As such, sinusoidal functions can be used to describe any phenomenon that displays a wave or wave-like pattern or by extension any predictable periodic behavior. 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