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1-2: Graphs and Lines Objectives: 1. Slopes 2. Graph line equations 3. x- and y-intercepts 4. Find the equation of a line in 3 forms 5. Vertical and horizontal lines How to find slope of a line: EX: Find the slope of the line passing through the given two points: a. (-2, 7) and (-3, -1) b. (8, 2) and (3, 4) Note: If m > 0 (slope is positive), the line rises from left to right; If m < 0 (slope is negative), the line falls from left to right; Definition: A linear equation in two variables is an equation that can be written in the standard form: Note: No fractions in standard form! Ex: How many points are needed to graph a line equation? It’s easy to use two special points: Using intercepts to graph • x-intercept: the point where the graph intersects the x-axis. To find x-intercepts, let = 0 and solve for . Always express as an ordered pair (x, 0) • y-intercept: the point where the graph intersects the y-axis. To find y-intercepts, let = 0 and solve for . Always express as an ordered pair (0, y) Ex graph 2x – 3y = 6. Ex: graph 4x + 2y = 0 Note:The x- and y-intercept is the same point – which is not enough to graph a line. You need another point! Pick any x-value & plug it in & solve for y. Three forms of a line: 1. Point-slope form: Advantage: works with any point, not just yintercept. 2. Slope-intercept form: 3. Standard form: Ax + By = C (A, B, C are integers) Ex: a) Write an equation of a line w/slope -3/7 and y-intc (0, 2) b) Write an equation of a line passing through (-2, 1) and (0, 5) Note: An equation in standard form can easily be put into slope-intercept form by simply solving for y. Ex: Ex: Write an equation of a line w/slope -1/2 going through (3, -2). Give all three forms. Ex: Find the standard form and slope-intercept form of the equation of the line that passes through the points (3, -2) and (7, 4) Special lines: Vertical line: Horizontal Line: Ex (vertical/horizontal lines) Write the equation of the vertical and horizontal lines through the point (6, -5). Ex (Finding information about a line with graph given) Use the graph of each line to find x-intercept, yintercept, and slope. Write the slope-intercept form of the equation of the line. Applications Ex The management of a company that manufactures skateboards has fixed cost (cost at 0 output) of $300 per day and total cost of $4,300 per day at an output of 100 skateboards per day. Assume that cost C is linearly related to output x. A) Find an equation of the line relating output to cost. Write the final answer in the form C = mx + b; B) Graph the cost equation from part A) for 0 ≤ x ≤ 200 . Practice Problems: 1. Find the slope of the line represented by the equation 3x – 2y = 6 2. Write the equation of the line that passes through points with coordinates (4, 2) and (-2, -6). Write this equation in point slope form, slope intercept form and standard form. Answers to practice problems: 1. 3/2 2. y – 2 = 4/3(x - 4), y = 4/3x – 10/3, 4x – 3y = 10