# Developmental Math

by Maribeth
(Draper, South Dakota)

Find the equation of line b described below, in slope intercept form.

Line a is parallel to line b.

Line a passes through points (5,7) & (-1,-2).

Line b passes through points (11,-5).

 Aug 18, 2013 Linear Equation by: Staff AnswerPart ISince line b is parallel to line a, the slope of line b is equal to the slope of line a.Determine the slope of line “a”.slope = "rise" over "run", or "rise" DIVIDED BY "run"slope = (change in "y" values)/(change in "x" values)slope = Δy / Δxslope = (y₂ - y₁)/(x₂ - x₁) The x-y coordinates for the two points for Line “a” are However, these two points are must be listed in the proper order (left to right).The two points should be listed as (-1, -2) and (5, 7) because the slope will be calculated as the change of "y" when x increases. In this case "x" will increase from -1 to 5 (left to right).Calculation of the slope for Line “a” Points: Left and Right(-1, -2) and (5, 7)(x₁, y₁) and (x₂,y₂)x₁ = -1x₂ = 5y₁ = -2y₂ = 7slope = (y₂ - y₁)/(x₂ - x₁)slope = (7 - (-2))/(5 - (-1))slope = (7 + 2)/(5 + 1)slope = (9)/(6)slope = 3/2 -----------------------------------------------------------

 Aug 18, 2013 Linear Equation by: Staff ----------------------------------------------------------- Part II Write the equation of line “b”. The Point-Slope Form ```Point-Slope Form: (y - y₁) = m (x - x₁) This format uses a single known point (x₁,y₁) and the slope m (which is also a known value) From the problem statement: m (the slope) = 3/2 single known point (x₁,y₁) = (11,-5) x₁ = 11 y₁ = -5 (y - y₁) = m (x - x₁) (y - (-5)) = (3/2)*(x - 11) ``` -----------------------------------------------------------

 Aug 18, 2013 Linear Equation by: Staff ----------------------------------------------------------- Part III Point Slope Form of Equation for Line “b”: (y + 5) = (3/2)*(x - 11) The Slope Intercept Form ```Slope Intercept Form y = mx + b (y + 5) = (3/2)*(x - 11) 2*(y + 5) = 2*(3/2)*(x - 11) 2y + 10 = 3x - 33 2y + 10 - 10 = 3x - 33 - 10 2y + 0 = 3x - 43 2y = 3x - 43 2y / 2 = (3x - 43) / 2 y = (3/2)x - 43/2 Slope Form of Equation for Line “b”: y = (3/2)x - 43/2 ``` -----------------------------------------------------------

 Aug 18, 2013 Linear Equation by: Staff ----------------------------------------------------------- Part IV Thanks for writing. Staff www.solving-math-problems.com