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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 2 y= x+4 3 Subtract 2x to both sides. Divide by –3 to both sides. Now we can choose values for x to find values for y. XY 3 6 0 4 -3 2 2 y = (3) + 4 23 y = (0) + 4 3 y=2+4 y=4 PLOT y= 2 (-3) + 4 3 y = -2 + 4 NOW GRAPH A LINE y=2 y=6 Graph a linear equation Graph: 3x – 4y = 8 Solve for y so the equation looks like y = mx + b - 4y = -3x + 8 3 y= x–2 4 Subtract 3x to both sides. Divide by –4 to both sides. Now we can choose values for x to find values for y. XY 3 4 1 y = (4) -2 4 0 -2 y = 3 (0) - 2 4 -4 -5 y=3-2 y = -2 PLOT y= 3 (-4) - 2 4 y = -3 - 2 NOW GRAPH A LINE y = -5 y=1 Graph a linear equation Graph: 3x = 6 X=2 Missing a y term, so solve for x 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) Graph a linear equation Graph: -4y = 12 Y = -3 Missing a x term, so solve for y 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) Graph a linear equation using x and y intercepts. Graph: 2x – 3y = -12 Let x = 0 2(0) – 3y = -12 Now let y = 0 2x – 3(0) = -12 2x – 0 = -12 2x = -12 0 - 3y = -12 -3y = -12 y=4 x = -6 x intercept is (-6, 0) y intercept is (0, 4) PLOT NOW GRAPH A LINE Graph a linear equation using x and y intercepts. Graph: -5x + 3y = -15 -5(0) + 3y = -15 Let x = 0 Now let y = 0 -5x + 3(0) = -15 -5x + 0 = -15 -5x = -15 0 + 3y = -15 3y = -15 y = -5 x=3 x intercept is (3, 0) y intercept is (0, -5) PLOT NOW GRAPH A LINE 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 2 y= x+4 3 Subtract 2x to both sides. Divide by –3 to both sides. Now the equation is in y = mx + b form called slope y-intercept form. 2 m is the slope of the line 3 and b is the y-intercept (0, 4) Now plot the y-intercept (0, 4) 2 The slope of the line is so from the coordinate (0, 4) 3 go up 2 lines, then move right 3 lines and plot a 2nd point. UP 2 RIGHT 3 NOW GRAPH A LINE 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 3 . 5 Plot the point (-4, 5) Now from the point (-4, 5) the slope is 3 , 5 so go down 3 lines and then right 5 lines. DOWN 3 RIGHT 5 Now graph the line