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Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
(1)
Rearrange 3x + 2y = 1 into this form by subtracting 3x from both sides
2y = - 3x + 1 ( divide all terms by 2 )
y = - x +
← in slope- intercept form
with slope m = -
Parallel lines have equal slopes, thus
y = - x + c ← is the partial equation
To find c substitute (- 6, 15) into the partial equation
15 = 9 + c ⇒ c = 15 - 9 = 6
y = - x + 6 ← equation of line
(2)
Rearrange x + 2y = 8 into slope- intercept form by subtracting x from both sides
2y = - x + 8 ( divide all terms by 2 )
y = - x + 4 ← in slope- intercept form
with slope m = -
Given a line with slope m then the slope of a line perpendicular to it is
= -
= -
= 2, thus
y = 2x + c ← is the partial equation
To find c substitute (5, - 2) into the partial equation
- 2 = 10 + c ⇒ c = - 2 - 10 = - 12
y = 2x - 12 ← equation of line