Please help! Find the equation of the line.
1 answer:
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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
Check the picture below.
since chords NQ and MP cross the center of the circle at R, that means that those two chords are diametrical chords and the angles made by both are vertical angles and thus twin angles, namely both are 18° as you see in the picture, so the angle NMP in magenta is really 162° + 18° + 18° = 198°, and we know the radius NR is 8.
