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Writing linear equations

Learn how to write linear equations using the slope-intercept form (y = mx + b) and point-slope form given a point and slope. Understand the roles of slope (m) and y-intercept (b) in the equation, and acquire skills to calculate the equation of a line from different scenarios, including two points on the line. This guide will walk you through examples, demonstrating how to substitute values into the equation and solve for unknown variables, ensuring you grasp essential concepts of linear equations.

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Writing linear equations

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  1. Writing linear equations 5.1 and 5.2

  2. Writing a linear equation given the slope and y-intercept • Use the equation y = mx + b • The slope is the m in the equation. • The b is the y-intercept in the equation. • The equation of your line should be in the form y = #x + # where you have filled in for the missing #’s Slope = 5 and the y-intercept = -3 y = 5x - 3 slope y-intercept

  3. Writing a linear equation given a point and the slope. • Use the equation y = mx + b • The slope is your m in the equation. • The point is your x and y in y = mx + b. • The only part of the equation that you do not know is b, so you must find it. • Substitute in x, y, and m into y = mx + b and solve for b. • After finding b, go back to y = mx + b and substitute in the value of b and the slope. (4,5), slope = Substitute in m and b y = x + 4 5 = (4) + b 5 = 1 + b -1 -1 m b 4 = b

  4. Writing a Linear equation with two points • Find the slope of the line with the slope equation • Find the b value by picking one of the given points and substituting x, y, and b into y = mx + b. • Substitute m and b into y = mx + b (-8, 84), (5, -46) = -10 = m Pick point -46 = -10(5) + b Substitute in m and b y = -10x + 4 -46 = -50 + b +50 +50 4 = b

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