Determine the equation of the line that represents the daily cost by the number of miles travelled and graph it.
Linear function graph plus#
Exercise 3Ī car rental charge is dollars per day plus dollars per mile travelled. If the plant continues to grow at this rate, determine the function that represents the plant's growth and graph it. It measured when it arrived at the nursery and exactly one week later. This means that y increases 2 units for every 1 unit of x.It has been observed that a particular plant's growth is directly proportional to time. Name the slope of each line, and state the meaning of each slope. The slope of a straight line - that number - indicates the rate at which the value of y changes with respect to the value of x. Therefore, since the variables x and y are the coördinates of any point on that line, that equation is the equation of a straight line with slope a and y-intercept b. Then if ( x, y) are the coördinates of any point on that line, its Therefore, let the slope of a line be a, and let the one point on it be its y-intercept, (0, b). Is the equation of a straight line with slope a and y-intercept b.įor, a straight line may be specified by giving its slope and Where A, B, C are integers, is called the general form of the equation of a straight line. Because, as we shall prove presently, a is the slope of the line ( Topic 8), and b - the constant term - is the y-intercept. Is called the slope-intercept form of the equation of a straight line. See Lesson 33 of Algebra, the section "Vertical and horizontal lines." To cover the answer again, click "Refresh" ("Reload").Īn equation of the form y = A number, is a horizontal line. To see the answer, pass your mouse over the colored area. Mark the x- and y-intercepts, and sketch the graph of (We will prove that below.) For that reason, functions or equations of the first degree - where 1 is the highest exponent - are called linear functions or linear equations.
And y = 2 x + 6 is called the equation of that line.Įvery first degree equation has for its graph a straight line. That line, therefore, is called the graph of the equation y = 2 x + 6. (That's what it means for a coördinate pair to be on the graph on any equation.) Every coördinate pair ( x, y) on that line is
It means that every coördinate pair ( x, y) that is on the graph, solves that equation. Now, what does it mean to say that y = 2 x + 6 is the "equation" of that line? Sketching the graph of a first degree equation should be a basic skill. Hence the student should know that the graph of any first degree polynomial y = ax + b is a straight line, and, conversely, any straight line has for its equation, y = ax + b. Skill in coördinate geometry consists in recognizing this relationship between equations and their graphs. A polynomial of the third degree has the form shown on the right. The graph of a second degree polynomial is a curve known as a parabola. The graph of a first degree polynomial is always a straight line. We will find that the graph of each degree leaves its characteristic signature on the x- y-plane. W E NOW BEGIN THE STUDY OF THE GRAPHS of polynomial functions. 9 LINEAR FUNCTIONS The Equation of a Straight Line
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