71 R eview of Graphs and Slopes of Lines课件.pptVIP

7.1 Review of Graphs and Slopes of Lines Standard form of a linear equation: The graph of any linear equation in two variables is a straight line. Note: Two points determine a line. Graphing a linear equation: Plot 3 or more points (the third point is used as a check of your calculation) Connect the points with a straight line. 7.1 Review of Graphs and Slopes of Lines Finding the x-intercept (where the line crosses the x-axis): let y=0 and solve for x Finding the y-intercept (where the line crosses the y-axis): let x=0 and solve for yNote: the intercepts may be used to graph the line. 7.1 Review of Graphs and Slopes of Lines If y = k, then the graph is a horizontal line (slope = 0): If x = k, then the graph is a vertical line (slope = undefined): 7.1 Review of Graphs and Slopes of Lines Slope of a line through points (x1, y1) and (x2, y2) is: Positive slope – rises from left to right.Negative slope – falls from left to right 7.1 Review of Graphs and Slopes of Lines Using the slope and a point to graph lines:Graph the line with slope passing through the point (0, 0)Go over 5 (run) and up 3 (rise) to get point (5, 3) and draw a line through both points. 7.1 Review of Graphs and Slopes of Lines Finding the slope of a line from its equation: Solve the equation for y The slope is given by the coefficient of x Parallel and perpendicular lines: Parallel lines have the same slope Perpendicular lines have slopes that are negative reciprocals of each other 7.1 Review of Graphs and Slopes of Lines Example: Decide whether the lines are parallel, perpendicular, or neither: solving for yin first equation: solving for yin second equation: The slopes are negative reciprocals of each other so the lines are perpendicular 7.2 Review of Equations of Lines Standard form: Slope-intercept form:(where m = slope and b = y-intercept) Point-slope form: The line with slope m going through point (x1, y1) has the equation: 7.2 Review of Equations of Lines Example: F