71 R eview of Graphs and Slopes of Lines.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: Find