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Additional resources for Advanced Mathematical Concepts: Precalculus with Applications
Y 3x ϩ 4y Ϫ 12 ϭ 0 O x Example The solutions of a linear equation are the ordered pairs for the points on its graph. An ordered pair corresponds to a point in the coordinate plane. Since two points determine a line, only two points are needed to graph a linear equation. Often the two points that are easiest to find are the x-intercept and the y-intercept. The x-intercept is the point where the line crosses the x-axis, and the y-intercept is the point where the graph crosses the y-axis. In the graph above, the x-intercept is at (4, 0), and the y-intercept is at (0, 3).
In addition to raising grain, cotton and other fibers, fruits, or vegetables, farmers also work on dairy farms, poultry farms, horticultural specialty farms that grow ornamental plants and nursery products, and aquaculture farms that raise fish and shellfish. 5%. 5%. What was the average rate of decline? This problem will be solved in Example 2. • Graph linear equations. • Find the x- and y-intercepts of a line. • Find the slope of a line through two points. • Find zeros of linear functions. The problem above can be solved by using a linear equation.
Explain the significance of m and b in y ϭ mx ϩ b. y 2. Name the zero of the function whose graph is shown at the right. Explain how you found the zero. O x 3. Describe the process you would use to graph a line with a y-intercept of 2 and a slope of Ϫ4. 4. Compare and contrast the graphs of y ϭ 5x ϩ 8 and y ϭ Ϫ5x ϩ 8. Guided Practice Graph each equation using the x - and y -intercepts. 5. 3x Ϫ 4y ϩ 2 ϭ 0 6. x ϩ 2y Ϫ 5 ϭ 0 Graph each equation using the y- intercept and the slope. 7. y ϭ x ϩ 7 8.
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