Answer to Question #141968 in Analytic Geometry for Nade

Question

write an equation of the line that passes through point P and parallel to the line with the given equation P(0,-1), y = -2x + 3

M=

B=

P(-7,-4),y=16

M=

B=

P(-2,1),10x+4y=-8

M=

B=

p(0,0)y=-9x-1

M=

B=

Answer 1

$\displaystyle \textsf{By the law of parallelism,}\\ \textsf{two parallel lines have}\\ \textsf{the same gradient}\\ (a)\\ P(0,-1), \, y = -2x + 3\\ m = -2\\ \frac{y - (-1)}{x - 0} = -2\\ y + 1 = -2x\\ y = -2x - 1\\ m = -2\\ B = -1\\ (b)\\P(-7,-4),\, y=16\\ m = 0\\ \frac{y - (-4)}{x - (-7)} = 0\\ y + 4 = 0\\ y = -4\\ m = 0\\ B = -4\\ (c)\\ P(-2,1),\, 10x+4y=-8\\ 4y = 8 - 10x\\ y = 2 - \frac{5x}{2}\\ m = -\frac{5}{2}\\ \frac{y - 1}{x - (-2)} = -\frac{5}{2}\\ y - 1 = -\frac{5}{2}(x + 2)\\ 2y - 2= -5x - 10\\ 2y + 5x = -8\\ y = -4 - \frac{5x}{2}\\ m = -\frac{5}{2}\\ B = -4\\ (d)\\ p(0,0), \, y=-9x-1\\ m = -9\\ \frac{y - 0}{x - 0} = -9\\ y = -9x\\ m = -9\\ B = 0\\$