2 Solution of a Linear Equation Is an ordered pair (x, y) that makes the equation true.Example: Determine whether the ordered pair is a solution of x + 2y = 5.a) (1, 2) b) (7, -3)
3 Writing Linear Equations in Slope-Intercept Form An equation is in slope intercept form when “y” is isolated (it is by itself on one side of the equal sign).y = mx + b
4 Example 2: Write the equation in slope – intercept form -2x + y = -3
5 You Try It…Write each equation in slope-intercept form. Then identify the slope and the y-intercept.-3x + y = 122) 4y – 2x = 83) 5x + 2y + 15 = 04) -5x – 3y = 12
6 Graphs of Linear Equations The graph of an equation in x and y is the set of ALL points (x, y) that are solutions to the equation.The graph of a linear equation can be shown to be a straight line.
7 We can use Slope-Intercept form to Graph Equations Steps:1) Write the equation in slope-intercept form (get “y” alone).2) Identify slope (m) and y-intercept (b).3) Plot the y-intercept.4) Use the slope (rise/run) to plot at least 2 more points).5) Connect all points with a straight line (USE A RULER!).
8 Example 3 Find the slope and y-intercept of y = -3x + 2 Then graph the equation.
9 Example 4 Find the slope and y-intercept of 2x – y = -3 Then graph the equation.
10 You Try It… Find the slope and y-intercept of each equation. Then graph the equation.y = -2xy = 4x – 5y = x + 2
11 ApplicationAndrew has a small business making decorated hats. Based on data for the last eight months, he calculates his monthly cost y of producing x hats using the equation y = 1.9xA) Explain what the y-intercept and the slope mean in this model.B) graph the model. Then use the graph to estimate the cost of 35 hats.