What is the relation between a and b for which the lines 3x + ay = 16 is parallel to bx - y = 5

Expert Answers

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The equation of a straight line in the slope-intercept form is y = mx + b where m is the slope of the line and b is the y-intercept. Two parallel lines have the same slope. 

Write the given equations in the slope intercept form:

3x + ay = 16

=> ay = 16 - 3x

=> y = (-3/a)*x + 16/a

bx - y = 5

=> y = bx - 5

The slope of the lines is (-3/a) and b respectively. Equating these give: -3/a = b

=> a*b = -3

The relation between a and b for which the lines 3x + ay = 16 and bx - y = 5 are parallel is a*b = -3

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