Line CD passes through points C(3, –5) and D(6, 0). What is the equation of line CD in standard form?

1 answer:

5 0

Slope = (y₂- y₁) / (x₂- x₁)

Points C( 3, -5) and D (6, 0) compare to (x₁, y₁) and (x₂, y₂)

Slope = (0 - -5) / (6- 3) = (0+5) / (3) = 5/3

Slope = 5/3

Equation of line given a slope and point, y - y₁ = m(x - x₁)

m = 5/3,    let point C( 3, -5) = (x₁, y₁)

y - - 5 = (5/3) (x - 3)

y + 5 = (5/3)(x - 3)

   3(y + 5) = 5(x - 3)

3y + 15 = 5x - 15

   3y = 5x - 15 - 15

   3y = 5x - 30

Hence the equation of the line is 3y = 5x - 30

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Nigel travels a total of 312 miles to school each day. He walks 14 mile to the bus stop. He travels 234 miles on the city bus. I

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The bus drops Nigel off 64 miles away from the school.

Step by step Explanation:

An equation for this would be 312-14-234 (this was the equation I used. Since you would do left to write to solve the equation, you would do, 312-14 which equals 298. Then, the equation is left as 298-234, and when you solve that part to the equation, yoh would be getting 64. And that's how you would get the answer 64miles away from the school.

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Using the given information, give the vertex form equation for each parabola.

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Answer:

Step-by-step explanation:

If you plot this point and the directrix on a coordinate plane, you can see that the directrix is 1/4 of a unit below the vertex. Since, by nature, a parabola opens in the direction opposite the directrix and "hugs" the focus, this is a positive x-squared parabola (meaning it opens upwards). The formula for this type of a parabola is, in vertex form,

$4p(y-k)=(x-h)^2$

where p is distance (in units) between the vertex and the directrix and h and k are the coordinates of the vertex. For us, p = .25, h = 7, and k = -6. Filling in our formula:

$4(.25)(y+6)=(x-7)^2$