Mathematics, 17.07.2019 08:30 roibeyj

What is an equation of the line that is perpendicular to -4/5x+3 and passes through the point(4, 12)

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Now, for the equation that we're trying to find, all that they give us is their slope, and a point that it passes through. How do we get the slope? Perpendicular line's slopes are negative reciprocals of each other. This means that you flip the coefficient of the x around, and multiply it by negative 1. So, we see that the given slope of the other line is -4/5. That means, we flip it around (-5/4), them multiply it by -1, which means the slope of our new line is 5/4. Now, we have the x, but what do we do with the point? We plug it into the point-slope formula

y-y1=m(x-x1) , where m = slope, and (x1,y1)

Our slope (m) is 5/4, our x1 is 4, and our y2 is 12 (these are the points given to us in the original problem, (4,12).)

Now, we plug it in, then get y by itself

y-y1=m(x-x1)
y-(12)=(5/4)(x-4)
y-12=5/4(x-4)
y=5/4(x-4)+12
y=5/4x-5+12
y=5/4x+7

So, our new equation is

y=5/4x+7

Answer from: Quest

answer: rlly

step-by-step explanation:

Answer from: Quest

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

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