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3-6 Lines in the Coordinate Plane Slope-intercept formula y = mx + b m and b are numbers. y and x will stay letters. m is the slope, b is the y-intercept. This is where the line crosses the y-axis 3 y x 2 5 Ex: 3 m b 2 5 Given m = 4 b = 8, put in slope-intercept form y = 4x + 8 Point-slope formula—used when you know the slope and a point on the line or two points. Solving for y in point-slope formula puts the equation in slope-intercept form. y and x remain letters. y1, x1, and m are letters. m is the slope. x1 and y1 are point’s coordinates (x1, y1) Example Given m = 2 and (3, -4) put in slope intercept form y – (-4) = 2 (x - 3). Now “clean up” the double negative y + 4 = 2 (x -3) To put in slope-intercept form: Distribute the 2 y+ 4 = 2x -6 y = 2x -10 Example: Given two points, give the equation of the line in slope intercept form. (6, -4) ( 8, 2) First, find the slope 2 – (-4) = 2+4 = 6 = 3 8 -6 2 2 Next, pick one of the points and use point-slope formula. You will get the same answer for either point. If a point has a 0 in it, pick it—this is less work. y – 2 = 3(x -8) y – 2 = 3x -24 y = 3x – 22 y – (-4) = 3 (x – 6) y + 4 = 3x - 18 y = 3x - 22