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Sec. 3-6 Lines in the Coordinate Plane

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

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Sec. 3-6 Lines in the Coordinate Plane

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  1. Sec. 3-6Lines 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 y – intercept (where the line crosses the y-axis y = mx + b y - coordinate x - coordinate • Slope • symbol is (m) • Rise/Run = Δy/Δx = (y2 – y1) (x2 – x1)

  4. To graph using slope intercept form: 1) Make it look like y = mx + b 2) Graph y – intercept (b) 3) Check to see if your slope is negative or positive 4) Decide if your line is increasing or decreasing (which way it slants) 5) Count your slope off to find your next point 6) Connect the 2 points to make the line of your equation 7) Confirm your line slants in the right direction.

  5. Example1: Graph the following equation using the slope intercept method. -6x + 3y = 12 3y = 6x + 12 y = 2x + 4

  6. II. Graphing using Point – Slope form • Must be a non-vertical Line! • Use this when given a slope and a point. y – y1 = m(x – x1) Slope of line y – coordinate of point x – coordinate of 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 Y1 - coordinate X1 -coordinate

  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 6 -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 Now pick one point and use the slope and plug it into the point-slope equation. y – y1 = m(x – x1) y – 1 = -2(x – (-1)) y – 1 = -2x - 2 y = -2x -1 X1 y1 x2 y2

  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. m = 3 m = 1 m = 2 m = 1/2 m = 1/3

  12. Horizontal Lines • A horizontal line has the same y value all the way across. • The x value doesn’t matter! y = 3 4 2

  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 don’t matter. x = 6 5 7

  14. Example: Graph the line with the following equation: y = -3 • First is the line horizontal or vertical? Horizontal Line -2 y = -3 -4

  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 Youuse 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. x = -10 -11 -9

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