line n is perpendicular to y=-3/4x +5 and goes through point (9,10) write line n in standard form

Answer:8x + 6y + 12 = 0Step-by-step explanation:If n is perpendicular to y=-3/4x +5, its slope is the reciprocal.The reciprocal is when the fraction is flipped and neg/pos is switched.m = -3/4 => m=4/3Substitute m=4/3 and point (9,10) into the equation of a line in slope-intercepty = mx + b10 = (4/3)(9) + b10 = 36/3 + b10 = 12 + bb = -2Slope of the line in slope-intercept form is y = 4/3x -2To convert slope-intercept form to standard form:y = mx + by = (-ax - c)/b <=this is a different bax + by + c = 0y = 4/3x -2-2 = -c/b(4/3) = -a/bfor the equation to work we can set b=6.-c/b = -2-c/6 = -2-c/6 = -12/6c = 124/3 = -a/b4/3 = -a/6-a = 8a = 88x + 6y + 12 = 0