# Linear equations - standard form, slope intercept form, point-slope form

(a) Rewrite the following linear equation in the standard form, slope intercept form, and point-slope form. (b) Identify the slope and the y intercept.

2y = 4x + 16

### Comments for Linear equations - standard form, slope intercept form, point-slope form

 Jun 27, 2012 Linear equations by: Staff The answer: Summary for formats: Standard Form: Ax + By = C A, B, and C are constants Slope Intercept Form: y = mx + b m = slope b = y intercept 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) 2y = 4x + 16 Standard Form: Ax + By = C 2y = 4x + 16 2y - 4x = 4x - 4x + 16 2y - 4x = 0 + 16 >>> 2y - 4x = 16, Standard Form Slope Intercept Form: y = mx + b 2y = 4x + 16 2y / 2 = (4x + 16) / 2 y * (2/ 2) = (4x + 16) / 2 y * (1) = (4x + 16) / 2 y = (4x + 16) / 2 y = 4x / 2 + 16 / 2 y = (4/2)x + 16 / 2 >>> y = 2x + 8, Slope Intercept Form >>> m (the slope) = 2 >>> b (the y intercept) = 8 Point-Slope Form: (y - y₁) = m (x - x₁) 2y = 4x + 16 Compute two points (x₁,y₁) and (x₂,y₂). Both points are needed to compute the slope “m”. If x₁ = 0 2y₁ = 4x₁ + 16 2y₁ = 4*0 + 16 2y₁ = 0 + 16 2y₁ = 16 2y₁ / 2 = 16 / 2 y₁*(2 / 2) = 16 / 2 y₁*(1) = 16 / 2 y₁ = 16 / 2 y₁ = 8 (x₁,y₁) = (0, 8) If x₂ = 1 2y₂ = 4x₂ + 16 2y₂ = 4*1 + 16 2y₂ = 4 + 16 2y₂ = 20 2y₂ / 2 = 20 / 2 y₂*(2 / 2) = 20 / 2 y₂*(1) = 20 / 2 y₂ = 20 / 2 y₂ = 10 (x₂,y₂) = (1, 10) Slope “m” m = (y₂ - y₁) / (x₂ - x₁) m = (10 - 8) / (1 - 0) m = 2 / 1 m = 2 (y - y₁) = m (x - x₁) >>> (y - 8) = 2 (x - 0), Point-Slope Form Thanks for writing. Staff www.solving-math-problems.com