Part I: Find the slope of the line that passes through the following points. (6 points; 2 points each) A (10, 4) and B (–2, –5) C (–7, 1) and D (7, 8) E and F ———
Part II: Robert says that the slope of a line passing through (1, 7) and (3, 9) is equal to the ratio . Is this a correct method for calculating the slope? Explain your answer. (1 point)

Part III: Do the points in the following set lie on the same line? Explain your answer. Show all work. (4 points) A (1, 3) B (4, 2) C (–2, 4)

In this exercise we have to use the knowledge of equations to calculate the points, in this way we can say that:

1.) 3/4, 1/7

2.) No.

3.) No.

So first we find that:

1.) The slope formula can be calculated as:

2.) The slope of a line passing through (1, 7) and (3, 9) will be:

Is not the correct method of calculating slope.

3.) Do not lie on the same lines. If they do, they will all have the Same value for x or the same value for y.

See more about slope at link

1.) Slope M are 3/4, 1/7

2.) No.

3.) No.

Step-by-step explanation:

1.) Slope M = change in y ÷ change in x

That is,

M = (y1 - y2)/(x2 -x1)

Given the following points:

A (10, 4) and B (–2, –5) C (–7, 1) and D (7, 8) E and F(-2, 2/3)

The slopeM between point A and B will be

M = (-5-4)/(-2-10)

M = -9/-12 = 3/4

The slope M between point C and D will be

M = (8-1)/(7+7)

M = 7/14 = 1/7

The slope M between point E and F will be

2.) The slope of a line passing through (1, 7) and (3, 9) will be

M = (9-7)/(3-1)

M = 2/2 = 1

But Robert say The ratio = (1-3)/(7-9) = 1

Though Robert will eventually get the Same value but that is not the correct method of calculating slope.

3.) Point A (1, 3) B (4, 2) C (–2, 4) do not lie on the same lines. If they do, they will all have the Same value for x or the same value for y.

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

this answer is !