259 2.5 Equations of Lines and Linear Models A summary of the various forms of linear equations follows. Summary of Forms of Linear Equations Equation Description When to Use y =mx +b Slope-Intercept Form Slope is m. y-intercept is 10, b2. The slope and y-intercept can be easily identified and used to quickly graph the equation. This form can also be used to find the equation of a line given a point and the slope. y −y1 =m1x −x12 Point-Slope Form Slope is m. Line passes through 1x1, y12. This form is ideal for finding the equation of a line if the slope and a point on the line or two points on the line are known. Ax +By =C Standard Form (If the coefficients and constant are rational, then A, B, and C are expressed as relatively prime integers, with A Ú 0.) Slope is -A B 1B≠02. x-intercept is AC A, 0B 1A≠02. y-intercept is A0, C BB 1B≠02. The x- and y-intercepts can be found quickly and used to graph the equation. The slope must be calculated. y =b Horizontal Line Slope is 0. y-intercept is 10, b2. If the graph intersects only the y-axis, then y is the only variable in the equation. x =a Vertical Line Slope is undefined. x-intercept is 1a, 02. If the graph intersects only the x-axis, then x is the only variable in the equation. Modeling Data We can write equations of lines that mathematically describe, or model, real data if the data change at a fairly constant rate. In this case, the data fit a linear pattern, and the rate of change is the slope of the line. EXAMPLE 7 Finding an Equation of a LineThat Models Data Average annual tuition and fees for in-state students at public four-year colleges are shown in the table for selected years and graphed as ordered pairs of points in Figure 51, where x = 0 represents 2013, x = 1 represents 2014, and so on, and y represents the cost in dollars. This graph of ordered pairs of data is a scatter diagram. 0 1 2 3 4 8000 8500 9000 9500 x y Year Cost (in dollars) Figure 51 Year Cost (in dollars) 2013 8070 2014 8312 2015 8543 2016 8778 2017 8804 Data from National Center for Education Statistics.
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