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Slope intercept formThe slope intercept form of a line is: y = mx + b and m is the slope and b is the y-intercept The goal of this lesson is to use the slope and a point to write the equation of a line in this form (y = mx + b) Example #1 Given m = 2 and b = 5, write the slope intercept form The equation is y = 2x + 5 Example #2 m =5 and (1, 6) This time we have m, but b is missing, so we have to find b. Since m= 5, y = mx + b becomes y = 5x + b Now, use (1, 6) to get b Since x = 1 and y = 6, you can replace them into the equation. Substituting 1 for x and 6 for y gives 6 = 5×1 + b 6 = 5×1 + b is just a linear equation that you can solve to get b 6 = 5×1 + b 6 = 5 + b Subtract 5 from both sides 6 − 5 = 5 − 5 + b 1 = 0 + b 1 = b Now since we have b, y = 5x + 1 Example #3 (2, 3) and (4, 9) This time both m and b are missing, so the first thing to do is to get m and then use m and a point either (2, 3) or (4, 9) to get b Let x1 = 4, y1 = 9 and x2 = 2, y2 = 3 m = (y1 − y2) / (x1 − x2) = (9 − 3)/(4 − 2 ) = 6/2 = 3 Now we can use the value for m and one point to get b as already done in example #2 Although you have two points, It does not matter which point you choose. Since both points are on the line, they will yield similar results Choosing (2, 3), x = 2 and y = 3 Substituting 2 for x, 3 for y, and 3 for m into the equation y = mx + b we get: 3 = 3 × 2 + b 3 = 6 + b Subtract 6 from both sides 3 − 6 = 6 − 6 + b -3 = 0 + b -3 = b Now we have b = -3 and m = 3, y = 3x + -3
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