Find an equation of the line perpendicular to y = - 2x + 2
1 answer:
Answer:
<u><em>y = (1/2)x + 1</em></u>
Step-by-step explanation:
y=mx+b, where m is the slope and b the y-intercept (the value of y when x = 0). We are given y = -2x + 2 as the reference line and are asked to find a line that is perpendicular to it. (We'll get to the (2,2) thing later).
A perpendicular line has a slope that is the negative inverse of the reference line slope, which in this case is -2 (the m). The negative inverse of -2 is -(-1/2) or (1/2), This measn the perpendicular line will have the form:
y = (1/2)x + b
The complication is that we want this new line to go through point (2,2). Easy. Just substitute (2,2) in the aboove ea=quation and solve for b:
y = (1/2)x + b for (2,2)
<u>2</u> = (1/2)<u>2</u> + b
b = 2 - 1, b = 1
The equation of the line perpendicular to y = -2x + 2 is <u>y = (1/2)x + 1,</u>
<u></u>
See attached graph for proof.
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Answer:
option D is true.
Step-by-step explanation:
The right-angled triangle is shown.
From the right-angled triangle,
The angle Ф = 60°
We know that the trigonometric ratio
tan Ф = opposite / adjacent
- opposite = 4
- adjacent = n
Thus,
tan 60 = 4 / n
√3 = 4/n
n = 4/√3
Thus,
n = 4/√3
= (4 × √3) / (√3 × √3)
= 4√3 / 3
Thus,
n = 4√3 / 3
Using Pythagorean theorem
m = √n²+4²
Thus,
- n = 4√3 / 3
Therefore, option D is true.