Find the equation of the line that is perpendicular to y = –2x + 5 and contains the point
1 answer:
The given equation is:
To find the line perpendicular to it, we interchange coefficients and switch the signs of one coefficient.
The equation to a line perpendicular to it is:
$ 2y-x=c$
where, $c$ is some constant we have determine using the condition given.
It passes through $(2,-1)$
Put the point in our equation:
$2(-1)-(2)=c$
$c=-2-2$
$c=-4$
The final equation is:
$\boxed{ 2y-x=-4}$
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9514 1404 393
Answer:
Step-by-step explanation:
A lot of math is about matching patterns.
For example, ...
g(x) = f(x -h) +k
means g(x) is the function f(x) translated right by h units and up by k units. This will be true for any expression of f(x).
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In this problem, f(x) = √x. We want to translate it left 6 units (h=-6)*, and up 4 units (k=4).
The notation above means that we will replace x with (x-h) = x+6. and we will add k = 4 to the result.
f(x) = √x
g(x) = f(x+6) +4
g(x) = √(x+6) +4 . . . . . . matches choice D
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* Left is the opposite of right, so left 6 units is the opposite of right 6 units. h=6 for <em>right 6 units</em>, so h=-6 for <em>left 6 units</em>. Then x-h = x-(-6) = x+6.
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<em>Comment on the graph</em>
I find it useful to see a picture with these things. In the attached graphing calculator output, the blue curve is left 6 and up 4 from the red curve. The blue curve is g(x); the red one is f(x).
