Mathematics: PLEASE HELP ASA 1. Find the equation of the line through point (4,−7) and parallel to y=−2/3x+3/2. 2. Find the equation of the line through point (−1,4) and parallel to 5x+y=4 3. Find the equation of the line through point (5,4) and perpendicular to y=−4/3x−2 4. Find the equation of the line through point (8,−9) and perpendicular to 3x+8y=4

1/49Step-by-step explanation:...

PLEASE HELP ASA 1. Find the equation of the line

Ответ:

idk8348

29.01.2022

Mathematics

Step-by-step explanation:

Slope of parallel lines are equal.

1) m = -2/3

(4,-7)

$y-y_{1}=m(x-x_{1})\\\\y-[-7]=\frac{-2}{3}(x-4)\\\\y+7=\frac{-2}{3}*x-\frac{-2}{3}*4\\\\y+7=\frac{-2}{3}x+\frac{8}{3}\\\\y=\frac{-2}{3}x+\frac{8}{3}-7\\\\y=\frac{-2}{3}x+\frac{8}{3}-\frac{7*3}{1*3}\\\\y=\frac{-2}{3}x+\frac{8}{3}-\frac{21}{3}\\\\y=\frac{-2}{3}x-\frac{13}{3}$

2) 5x + y = 4

y = -5x + 4

slope m = -5

(-1,4)

y - 4 = -5(x -[-1])

y- 4 = -5(x+1)

y - 4 = -5x - 5

y = -5x - 5 + 4

y = -5x -1

If two lines are perpendicular, m2 = -1/m1

m1 = -4/3

$m_{2}=\frac{-1}{\frac{-4}{3}}=-1*\frac{-3}{4}=\frac{3}{4}\\$

(5,4)

$y-4=\frac{3}{4}(x - 5)\\\\y-4=\frac{3}{4}x-\frac{3}{4}*5\\\\y-4=\frac{3}{4}x-\frac{15}{4}\\\\y=\frac{3}{4}x-\frac{15}{4}+4\\\\y=\frac{3}{4}x-\frac{15}{4}+\frac{4*4}{1*4}\\\\y=\frac{3}{4}x-\frac{15}{4}+\frac{16}{4}\\\\y=\frac{3}{4}x+\frac{1}{4}$

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