3. Find the equation of a line that passes through the x-intercept of the line 3x+ 6y = 8 and is perpendicular to the line 2x - 5y = 10.​

y = -5/2x + 20/3

Step-by-step explanation:

x-int of 3x + 6y = 8

sub 0 for y

3x + 6(0) = 8

3x = 8

x = 8/3 or 2.667

line perpendicular to 2x - 5y = 10

put into y = mx + b form

2x - 5y - 10 = 0

5y = 2x - 10

y = 2/5 x - 2

find negative reciprocal of the slope 2/5 x (for the perpendicular line)

-5/2 x

find the y-int (b)

m = -5/2 x

must pass through (8/3,0)

y = mx + b

0 =  -5/2(8/3) + b

0 = -40/6 + b

b = 20/3

therefor the equation of the line is y = -5/2x + 20/3

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