Section 3.2 Graphing Linear Equations 221 Student Check 3 a. intercepts: (-2, 0) and (0, 8) b. intercepts: (1, 0) and (0, -3) c. intercepts: (0, 0) 8 2 0, 8 2 –2, 0 4 y –4 4 x 2 –4 –2 2 x 4 4 –2 –6 y 1, 0 0, –3 0, 0 –4 –2 2 4 x 1, –4 –2 –4 –6 y Student Check 4 a. y = -1 b. x = 5 c. 3y + 2 = 0 1 1 2 –1 –2 –1 –2 –3 x y 2 2 4 4 6 8 –2 –4 x y 4 2 –2 –4 x y –4 –2 2 4 Student Check 5 a. The y-intercept is (0, 27,645). This means that in 1990, the median annual income for women with a bachelor’s degree is $27,645. b. The median income in 2000 is $38,645 and was $49,645 in 2010. c. 60,000 50,000 30,000 20,000 10,000 0, 27,645 10, 38,645 20, 49,645 40,000 0 5 10 15 20 25 SUMMARY OF KEY CONCEPTS 1. A linear equation in two variables is an equation of the form Ax + By = C, where A, B, and C are real numbers with A and B not both zero. The exponent of the variables is one. If the values of A, B, and C are not fractions and A > 0, this form is called the standard form. It is important to be able to write equivalent forms of a linear equation in two variables. 2. To graph an equation by plotting points, select at least three different values for x or y, substitute into the equation, and solve for the corresponding value. These three points should lie in a straight line. If they do not, a mistake was made in your calculations or in graphing. 3. A linear equation can also be graphed by finding the x- and y-intercepts. a. To find the x-intercept, replace y with zero and solve for x. This is a point of the form (a, 0). b. To find the y-intercept, replace x with zero and solve for y. This is a point of the form (0, b). c. If both the x- and y-intercepts are (0, 0), then the graph goes through the origin. Another point is needed to graph the line. 4. Horizontal lines are represented by an equation of the form y = k. These lines have a y-intercept of (0, k). Equations of the form x = h have graphs that are vertical lines. These lines have an x-intercept of (h, 0). 5. When a linear equation is given that represents a reallife situation, the x- and y-intercepts have meaning. It is important to be able to state the meaning of these points. Finding other points and the graph of these models is also an important skill.
hendricks_beginning_intermediate_algebra_1e_ch1_3
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