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Graph a linear equation Graph: 2x – 3y = -12 Solve for y so the equation looks like y = mx + b - 3y = -2x – 12 Subtract 2x to both sides. y = x + 4 Divide by –3 to both sides. Now we can choose values for x to find values for y. X Y 3y = (3) + 4 y = 2 + 4y = 6 6 PLOT 0 y = (0) + 4y = 4 4 -3 y = (-3) + 4 y = -2 + 4 y = 2 2 NOW GRAPH A LINE

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Graph a linear equation Graph: 3x – 4y = 8 Solve for y so the equation looks like y = mx + b - 4y = -3x + 8 Subtract 3x to both sides. y = x – 2 Divide by –4 to both sides. Now we can choose values for x to find values for y. X Y 4y = (4) -2 y = 3 - 2y = 1 1 PLOT 0 y = (0) - 2y = -2 -2 -4 y = (-4) - 2 y = -3 - 2 y = -5 -5 NOW GRAPH A LINE

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Graph a linear equation Graph: 3x = 6 Missing a y term, so solve for x X = 2 Divide by 3 Now we can graph a line in which the value for x is 2 in all coordinates. Notice the line is vertical because every coordinate on the line has an x coordinate of 2. (2, 6) (2, 0) (2, -5)

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Graph a linear equation Graph: -4y = 12 Missing a x term, so solve for y Y = -3 Divide by -4 Now we can graph a line in which the value for y is -4 in all coordinates. Notice the line is horizontal because every coordinate on the line has a y coordinate of -4. (-3, -4) (0, -4) (3, -4)

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Graph a linear equation using x and y intercepts. Graph: 2x – 3y = -12 Let x = 0 2(0) – 3y = -12 0 - 3y = -12 PLOT NOW GRAPH A LINE -3y = -12 y intercept is (0, 4) Now let y = 0 2x – 3(0) = -12 2x – 0 = -12 2x = -12 x = -6 x intercept is (-6, 0) y = 4

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Graph a linear equation using x and y intercepts. Graph: -5x + 3y = -15 Let x = 0 -5(0) + 3y = -15 0 + 3y = -15 PLOT NOW GRAPH A LINE 3y = -15 y intercept is (0, -5) Now let y = 0 -5x + 3(0) = -15 -5x + 0 = -15 -5x = -15 x = 3 x intercept is (3, 0) y = -5

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Graph a linear equation, by using y intercept and slope. Graph: 2x – 3y = -12 Solve for y so the equation looks like y = mx + b - 3y = -2x – 12 Subtract 2x to both sides. y = x + 4 Divide by –3 to both sides. Now the equation is in y = mx + b form called slope y-intercept form. m is the slope of the line and b is the y-intercept (0, 4) NOW GRAPH A LINE Now plot the y-intercept (0, 4) The slope of the line is so from the coordinate (0, 4) go up 2 lines, then move right 3 lines and plot a 2 nd point. UP 2 RIGHT 3

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Graph a line given one point and the slope of the line. Graph the line that passes through the point (-4, 5) and has a slope of. Plot the point (-4, 5) Now from the point (-4, 5) the slope is, so go down 3 lines and then right 5 lines. DOWN 3 RIGHT 5 Now graph the line

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6.6 : General Form of the Equation for a Linear Relation

6.6 : General Form of the Equation for a Linear Relation

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