Problem

find the slope and y-intercept of the line that is  \green{\text{perpendicular}}perpend icularstart color #28ae7b, start text, p, e, r, p, e, n, d, i, c, u, l, a, r, end text, end color #28ae7b  to  \blue{y = -\dfrac{2}{3} x + 5}y=−32x+5start color #6495ed, y, equals, minus, start fraction, 2, divided by, 3, end fraction, x, plus, 5, end color #6495edand passes through the point  \red{(-6, -4)}(−6,−4)

The slope is 3/2 and y-intercept is 5.

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The question states:

Find the slope and y-intercept of the line that is perpendicular to

and passes through the point (-6, -4)

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From functions, we know that if two lines, called line 1 and line 2, are perpendicular, then it is true that:

If the given line is called line 1, then:

Then:

On the other hand, the y-intercept can be found as:

Find the slope is 3/2 and y-intercept is 5.

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