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Sec. 3-6 Lines in the Coordinate Plane

I. Linear Equations. The word linear means the graph will be a line.The line could be horizontal, vertical, or diagonal.3 ways to graph them.. I. Slope

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Sec. 3-6 Lines in the Coordinate Plane

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    1. Sec. 3-6 Lines in the Coordinate Plane Objectives: To graph lines given their equations To write equations of lines.

    2. I. Linear Equations The word linear means the graph will be a line. The line could be horizontal, vertical, or diagonal. 3 ways to graph them.

    3. I. Slope Intercept Form

    6. II. Graphing using Point Slope form Must be a non-vertical Line! Use this when given a slope and a point.

    7. Example: Graph a line that has a m = (-1/2) and runs through the point (2,-2). (2, -2) y y1 = m(x x1) y (-2) = (-1/2)(x 2) y + 2 = (-1/2)x +1 y = (-1/2)x - 1

    8. III. Graphing using x-intercepts and y-intercepts X-intercept Where the line crosses the x-axis. Y-intercept Where the line crosses the y-axis. Use this method any time you have the equation for the line. Step 1: To find the x-intercept, set y = 0. Step 2: To find the y-intercept, set x = 0.

    9. Example: Graph the equation 5x -6y = 30 using the its x & y intercepts. Find the x-intercept: Set y = 0 and solve. 5x -6(0) = 30 x = 6 Find the y-intercept: Set x = 0 and solve. 5(0) -6y = 30 y = -5

    10. Example: Write the equation of a line, in slope-intercept form of the line that runs through the points G(4,-9) and H(-1,1) Using the 2 points find the slope. (-1, 1) (4, -9) (y2 y1)/(x2 x1) = = (-9 1)/(4-(-1)) = -10/5 = -2 = m

    11. IV. Two special types of lines and their equations A horizontal line has a slope that = 0. A vertical line has a slope that is undefined.

    12. Horizontal Lines A horizontal line has the same y value all the way across. The x value doesnt matter!

    13. Vertical Lines A vertical line has a slope that is undefined. The line will have the same x value up and down the line. The y values dont matter.

    14. Example: Graph the line with the following equation: y = -3 First is the line horizontal or vertical? Horizontal Line

    15. What did I learn?? If I give you a point and a slope, how do I go about writing the equation for that line? Plug it into point slope equation. y y1 = m(x x1)

    16. If I give you 2 points, how do I go about writing the equation for the line? First you have to find the slope of the line that connects the 2 points: (y2 y1)/(x2 x1) = m Then You use that slope (m) and pick the first point and plug it into Point-slope equation. y y1 = m(x x1)

    17. What does y-intercept form look like? y = mx + b Write the equation for the following line.

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