What is an equation for the line perpendicular to y=-1/8x+6 that passes through (-3,-10)
1 answer:
Answer:
y = 8x + 14
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 )
y = - x + 6 ← is in slope- intercept form
with slope m = -
Given a line with slope m then the slope of a line perpendicular to it is
= -
= -
= 8 , then
y = 8x + c ← is the partial equation
To find c substitute (- 3, - 10 ) into the partial equation
- 10 = - 24 + c ⇒ c = - 10 + 24 = 14
y = 8x + 14 ← equation of perpendicular line
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9514 1404 393
Answer:
(8.49; 225°)
Step-by-step explanation:
The angle is a 3rd-quadrant angle. The reference angle will be ...
arctan(-6/-6) = 45°
In the 3rd quadrant, the angle is 45° +180° = 225°.
The magnitude of the vector to the point is its distance from the origin:
√((-6)² +(-6)²) = √(6²·2) = 6√2 ≈ 8.4859 ≈ 8.49
The polar coordinates can be written as (8.49; 225°).
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<em>Additional comment</em>
My preferred form for the polar coordinates is 8.49∠225°. Most authors use some sort of notation with parentheses. If parentheses are used, I prefer a semicolon between the coordinate values so they don't get confused with an (x, y) ordered pair that uses a comma. You need to use the coordinate format that is consistent with your curriculum materials.
