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Alex777 [14]
4 years ago
10

What is the point used in the equation of the line y+4=1/2(x-2)

Mathematics
1 answer:
Ket [755]4 years ago
8 0

Answer:

What is the point used in the equation of the line y+4=1/2(x-2)

The other format for straight-line equations is called the "point-slope" form. For this one, they give you a point (x1, y1) and a slope m, and have you plug it into this formula:

y - y1 = m(x - x1)

Don't let the subscripts scare you. They are just intended to indicate the point they give you. You have the generic "x" and generic "y" that are always in your equation, and then you have the specific x and y from the point they gave you; the specific x and y are what is subscripted in the formula. Here's how you use the point-slope formula

They've given me m = 4, x1 = -1, and y1 = -6.  I'll plug these values into the point-slope form, and solve for "y=":

y - y1 = m(x - x1)

y - (-6) = (4)(x - (-1))

y + 6 = 4(x + 1)

y + 6 = 4x + 4

y = 4x + 4 - 6

y = 4x - 2 

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Expand and simplify <img src="https://tex.z-dn.net/?f=%20%283x-2%29%5E%7B2%7D%20" id="TexFormula1" title=" (3x-2)^{2} " alt=" (3
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(3x - 2)^2 = (3x - 2)(3x - 2) =

Multiply every term of the first binomial by every term of the second binomial, then collect like terms. (This is often called using FOIL.)

= 9x^2 - 6x - 6x + 4

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2) Use the square of a binomial pattern

The square of a binomial is

(a - b)^2 = a^2 - 2ab - b^2

a^2 is the square of the first term.
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You have

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Put it all together, and you get

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