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Message: <blockquote data-quote="Lovtus" data-source="post: 28725248" data-attributes="member: 532745">1.1) Linear functionA linear function is a type of function in which the graph of the function is a straight line. Linear functions have the general form:f(x) = mx + bwhere m and b are constants, known as the slope and y-intercept, respectively.The slope of a linear function represents the rate of change of the function with respect to its input variable. It is defined as the change in the output variable divided by the change in the input variable, or:m = (y2 - y1) / (x2 - x1)where (x1, y1) and (x2, y2) are any two points on the line. The slope can also be interpreted as the amount by which the output variable changes for every unit change in the input variable.The y-intercept of a linear function represents the value of the function when the input variable is zero. It is the point where the line intersects the y-axis.--Eg.Problem 1: Given the linear function f(x) = 2x + 1, find the slope and y-intercept of the function.Solution: The slope of the function is the coefficient of x, which is 2. The y-intercept of the function is the constant term, which is 1. Therefore, the slope of the function is 2 and the y-intercept is 1.Problem 2: A car rental company charges a flat fee of $30 per day, plus an additional $0.25 per mile driven. Write a linear function that gives the total cost C as a function of the number of miles driven x.Solution: The flat fee of $30 is the y-intercept, and the additional charge of $0.25 per mile is the slope. Therefore, the linear function that gives the total cost C as a function of the number of miles driven x is:C(x) = 0.25x + 30Problem 3: The temperature at a certain location is decreasing at a rate of 2 degrees Fahrenheit per hour. Write a linear function that gives the temperature T as a function of time t in hours, assuming the initial temperature is 70 degrees Fahrenheit.Solution: The initial temperature of 70 degrees is the y-intercept, and the rate of decrease of 2 degrees per hour is the slope. Therefore, the linear function that gives the temperature T as a function of time t is:T(t) = -2t + 70Problem 4: A cell phone plan charges a flat fee of $30 per month, plus an additional $0.10 per minute of talk time. Write a linear function that gives the monthly cost C as a function of the number of minutes of talk time x.Solution: The flat fee of $30 is the y-intercept, and the additional charge of $0.10 per minute is the slope. Therefore, the linear function that gives the monthly cost C as a function of the number of minutes of talk time x is:C(x) = 0.10x + 30</blockquote>

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