272 Chapter 3 Linear Equations in Two Variables Use Function Notation to Represent Linear Equations in Two Variables We will now focus on a particular type of function, a linear function. Recall that the graph of Ax + By = C or y = mx + b is a line. All of these lines are also functions, except for vertical lines since they do not pass the vertical line test. Therefore, we can use function notation to write equations of non-vertical lines. When lines are written in the form y = mx + b, we can replace y with f (x) and put it in function notation. ������������������������ A function of the form f (x) = mx + b, for m and b real numbers is a linear function. ���������������������� Writing a Linear Equation in Two Variables in Function Notation Step 1: Solve the equation for y, if needed. Step 2: Replace y with f (x). �� ������������������������ ������������������ Write each linear equation in two variables in function notation. Then, find f (0), f (2), and f (-1) and write the corresponding ordered pairs. 5a. x + 2y = 4 5b. y = 7 Solutions 5a. x + 2y = 4 x + 2y - x = 4 - x Subtract x from each side. 2y=-x +4 Simplify. 2y 2 = -x 2 + 4 2 Divide each side by 2. y=- 1 2 x + 2 Simplify. f (x)=- 1 2 x + 2 Replace y with f (x). Now we must evaluate f (0), f (2), and f (-1). f (0)=- 1 2 (0) + 2 = 0 + 2 = 2 f (2)=- 1 2 (2) + 2=-1 + 2 = 1 f (-1)=- 1 2 (-1) + 2 = 1 2 + 2 = 1 2 + 4 2 = 5 2 The corresponding ordered pairs are (0, 2), (2, 1), and a-1, 5 2 b . 5b. The equation is already solved for y. So, in function notation, it is f (x) = 7. Recall that y = 7 is equivalent to y = 0x + 7. So, f (x) = 0x + 7. f (0) = 0(0) + 7 = 0 + 7 = 7 f (2) = 0(2) + 7 = 0 + 7 = 7 f (-1) = 0(-1) + 7 = 0 + 7 = 7 The corresponding ordered pairs are (0, 7), (2, 7), and (-1, 7). Student Check 5 Write each linear equation in two variables in function notation. Then find f (0), f (3), and f (-2) and write the corresponding ordered pairs. a. 2x + 3y = 6 b. y = 1 Objective 5 ▶ Write a linear equation in two variables in function notation.
hendricks_beginning_algebra_1e_ch1_3
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