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:
The domain is {x : x ∈ R} or (-∞ , ∞)
Step-by-step explanation:
* Lets explain how to find the domain
- The domain of the function is the values of x which make the
function defined
- The quantity under the square root must be ≥ 0 because there is
no square root for negative value
* Lets solve the problem
∵ f(x) = √(x² - x + 6)
∴ The value of (x² - x + 6) must be greater than or equal zero because
there is no square root for negative value
- Graph the function to know which values of x make the quantity
under the root is negative that means the values of x which make
the graph under the x-axis
∵ The graph doesn't intersect the x-axis at any point
∵ All the graph is above the x-axis
∴ There is no value of x make f(x) < 0
∴ x can be any real number
∴ The domain of f(x) is all real numbers
∴ The domain is {x : x ∈ R} or (-∞ , ∞)
