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kozerog [31]
3 years ago
8

What is the equation of a line in general form that passes through the point (1,-2) and has a slope of 1/3

Mathematics
1 answer:
ser-zykov [4K]3 years ago
4 0

Answer:

(y+2) = (1/3)(x-1)  

Answer in point-slope form, you can rearrange this into the form which you need.

Step-by-step explanation:

recall that the general point-slope form of a linear equation looks like :

(y - y₁) = m(x - x₁)

where m is the slope and (x₁,y₁) is any point on the line

here we are given m = 1/3 and (x₁,y₁)=(1,-2)

simply substitute this info into the general equation above

(y - y₁) = m(x - x₁)

(y - (-2) ) = (1/3)(x - 1)

(y+2) = (1/3)(x-1)  Answer in point-slope form, you can rearrange this into the form which you need.

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The parabola opens upward has x = 2 as an axis of symmetry and contains the non -vertex points (1, 9) and (4, 27) write the equa
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Answer:

<h3>               f(x) = 6(x - 2)² + 3</h3>

Step-by-step explanation:

f(x) = a(x - h)² + k    - vertex form of the equation of the parabola with vertex (h, k)

"the parabola opens upward" means:  a>0

"the parabola has x = 2 as an axis of symmetry" means:  h = 2

so f(x) = a(x - 2)² + k

"the parabola contains the point (1, 9)" means:

9 = a(1 - 2)² + k

9 = a(-1)² + k

9 = a + k

k = 9 - a

"the parabola contains the point (4, 27)" means:

27 = a(4 - 2)² + k

so:

27 = a(2)² + 9 - a

27 = 4a + 9 - a

3a = 18

a = 6

and  k = 9 - 6 = 3

Therefore the vertex form for this parabola is:

                                     <u> f(x) = 6(x - 2)² + 3</u>

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Step-by-step explanation:

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