Question #7f0f6

1 Answer
Feb 27, 2017

"the equation of the line is -2 x+3 y=13 or "y=2/3 x+13/3the equation of the line is -2 x+3 y=13 or y=23x+133

Explanation:

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color(blue)(2y+3x-4=0)" the equation of the blue line"2y+3x4=0 the equation of the blue line

"let's rearrange the equation of the blue line"let's rearrange the equation of the blue line

color(blue)(2y=-3x+4)2y=3x+4

color(blue)(y=-3/2 x+2) " (1)"y=32x+2 (1)

y=m x+n " represents the standard form of the line"y=mx+n represents the standard form of the line

"where m is slope of line"where m is slope of line

m=-3/2 m=32

"let the slope of the red line perpendicular to the blue line be " m_1let the slope of the red line perpendicular to the blue line be m1

m*m1=-1mm1=1

-3/2*m_1=-132m1=1

m_1=2/3m1=23

"now we can use the slope-intercept form of the equation of line"now we can use the slope-intercept form of the equation of line
color(red)(y-y_1=m(x-x_1)yy1=m(xx1)

color(red)(y-3=2/3(x+2))y3=23(x+2)

color(red)(y-3=2/3 x+4/3)y3=23x+43

color(red)(y=2/3 x+4/3+3)y=23x+43+3

color(red)(y=2/3 x+13/3)y=23x+133

"or "or

"let's multiply both sides of equation by 3"let's multiply both sides of equation by 3

3y=2x+133y=2x+13

-2x+3y=132x+3y=13