The answer is: "No; they are not parallel." <span>____________________________________________</span> Explanation: _____________________________________________ Given:
<span>y = 6x + 9 ; AND
27x - 3y = -81 ; __________________ We need to rewrite: __________________</span> " 27x - 3y = -81" ; in "slope-intercept form"; that is: " y = mx + b" ; and see if the "slope, "m" ; is the same as: "y = 6x + 9" ; or "6"; (that is, whether "m = 6"; when an equation is written is "slope-intercept form", the slope, "m", is the coefficient of "x"; and we are given an equation that is already written in: "slope-intercept form": __________________________________ " y = 6x + 9 " ; in which, the slope, "m", = "6". ___________________________________ If we can write the other equation given: __________________________________ " 27x - 3y = -81 " ; in "slope-intercept form"; and "m = 6"; (the same slope), then both equations are "parallel" to each other. _________________________________________ Given: ______ 27x - 3y = -81 ; _____________________ Let us write this in "slope-intercept form" ; _____________________________________ Let us multiply the ENTIRE equation (both sides) by "-1"; to get rid of most of the 'negatives' : ________________________________ -1* {27x - 3y = -81} ; __________________________ to get: ______________________________ -27x + 3y = 81 ; ______________________________ Now, add "27x" to EACH SIDE of the equation: ___________________________________ -27x + 3y + 27x = 81 + 27x ; _____________________________________ to get: 3y = 81 + 27x ; ↔ 3y = 27x + 81; _______________________________________ Now, divide the ENTIRE EQUATION (both sides) by "3"; to isolate "y" on the left-hand side of the equation; and to re-write the equation in "slope-intercept form: ______________________________________________________ 3y / 3 = (27x + 81) / 3 ; ________________________ y = 9x + 27 ; _________________________ So, y = mx + b ; m = "9"; which is not "6" ; ____________________________________ So the answer is: "No; they are not parallel." ____________________________________________
