What is the equation of a line that passes through the point (6, 1) and is perpendicular to the line whose equation is y=−2x−6 ?

If a line is perpendicular to another, it means that the slope of the first line is equivalent to the negative reciprocal of the second line. In simple terms, that means the slope of the first line is the same as -1 over the slope of the perpendicular line (-1/m).

So, we just need to do -1/-2 (as -2 is the slope of the perpendicular line) to work out the slope of the first line. -1/-2 is the same as 1/2, or 0.5.

Now, we know the equation of the first line is y = 1/2x + b.

We just need to substitute in the coordinates (6,1) respectively into the x and y values and we get:

(1) = 1/2(6) + b

Now let's simplify:

1 = 3 + b

Now we just need to find the y-intercept (which is b), and to do this, we just need to subtract 3 from both sides of the equation to isolate the b:

1 - 3 = b

-2 = b

Now that we know our b value, we just have to rewrite the whole equation, and you'll have your

y = 1/2x - 2

first, we define the variables:

x: number of years after 1950

f (x): amount of vinyl sold.

then, with the variables defined, we have:

68594 vinyl records were sold in 1958 > f (8) = 68594

91299 vinyl records were sold in 1961 > f (11) = 91299

38720 vinyl records were sold in 1952 > f (2) = 38720

161743 vinyl records were sold in 1967 > f (17) = 161743

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step-by-step explanation: