1. 1 PRECALCULUS I Dr. Claude S. Moore Danville Community College Graphs and Lines Intercepts, symmetry, circles Slope, equations, parallel, perpendicular

2. Equation - equality of two quantities. Solution - (a,b) makes true statement when a and b are substituted into equation. Point-plotting method - simplest way to graph. x -2-1012 y = 2x - 3-7-5-3-11 Graph of an Equation

3. The x-intercept is point where graph touches (or crosses) the x-axis. The y-intercept is point where graph touches (or crosses) the y-axis. 1. To find x-intercepts, let y be zero and solve the equation for x. 2. To find y-intercepts, let x be zero and solve the equation for y. Finding Intercepts of an Equation

4. 1. The graph of an equation is symmetric with respect to the y-axis if replacing x with -x yields an equivalent equation. 2. The graph of an equation is symmetric with respect to the x-axis if replacing y with -y yields an equivalent equation. 3. The graph of an equation is symmetric with respect to the origin if replacing x with -x and y with -y yields an equivalent equation. Tests for Symmetry

5. The point (x, y) lies on the circle of radius r and center (h, k) if and only if (x - h) 2 + (y - k) 2 = r 2. Standard Form of the Equation of a Circle

6. The graph of the equation y = mx + b is a line whose slope is m and whose y-intercept is (0, b). Slope-Intercept Form of the Equation of a Line

7. Definition: Slope of a Line The slope m of the nonvertical line through (x 1, y 1 ) and (x 2, y 2 ) where x 1 is not equal to x 2 is

8. The equation of the line with slope m passing through the point (x 1, y 1 ) is y - y 1 = m(x - x 1 ). Point-Slope Form of the Equation of a Line

9. 1. General form: 2. Vertical line: 3. Horizontal line: 4. Slope-intercept: 5. Point-slope: Equations of Lines 1. Ax + By + C = 0 2. x = a 3. y = b 4. y = mx + b 5. y  y 1 = m(x  x 1 )

10. Parallel: nonvertical l 1 and l 2 are parallel iff m 1 = m 2 and b 1  b 2. *Two vertical lines are parallel. Perpendicular: l 1 and l 2 are perpendicular iff m 1 = -1/m 2 or m 1 m 2 = -1. Parallel and Perpendicular Lines