Anya found the slope of the line that passes through the points (–7, 4) and (2, –3). her work is shown below. let (x2, y2) be (–7, 4) and (x1, y1) be (2, –3). m = = = the slope is . what error did she make? she simplified the denominator incorrectly. the denominator simplifies to –7. she labeled the points incorrectly. the point (–7, 4) should be (x1, y1). she used an incorrect formula. the formula should be the change in y-values with respect to the change in the x-values. she used an incorrect formula. the formula should be the sum of the x-values with respect to the sum of the y-values.

The formula should be the change in y-values with respect to the change in the x-values.

Step-by-step explanation:

Given that slope of the line passing through two points was found as per working shown.

We are to locate the error in the method

Slope of the line passing through two points =

Here (x2, y2) be (–7, 4) and (x1, y1) be (2, –3).

Hence numerator = 4-(-3) =7

and denominator = -7-2=-9

The formula should be the change in y-values with respect to the change in the x-values.

If we use this formula only we get correct slope.

But Anya used formula incorrectly.

answer: your correct answer is b. d.

step-by-step explanation:

i think it's eleven too, don't woosh me here, but according to the "experts" it's 2.

the proof starts from the peano postulates, which define the natural

numbers n. n is the smallest set satisfying these postulates:

  p1.   1 is in n.

  p2.   if x is in n, then its "successor" x' is in n.

  p3.   there is no x such that x' = 1.

  p4.   if x isn't 1, then there is a y in n such that y' = x.

  p5.   if s is a subset of n, 1 is in s, and the implication

      (x in s => x' in s) holds, then s = n.

then you have to define addition recursively:

  def: let a and b be in n. if b = 1, then define a + b = a'

      (using p1 and p2). if b isn't 1, then let c' = b, with c in n

      (using p4), and define a + b = (a + c)'.

then you have to define 2:

  def:   2 = 1'

2 is in n by p1, p2, and the definition of 2.

theorem:   1 + 1 = 2

proof: use the first part of the definition of + with a = b = 1.

      then 1 + 1 = 1' = 2   q.e.d.

note: there is an alternate formulation of the peano postulates which

replaces 1 with 0 in p1, p3, p4, and p5. then you have to change the

definition of addition to this:

  def: let a and b be in n. if b = 0, then define a + b = a.

      if b isn't 0, then let c' = b, with c in n, and define

      a + b = (a + c)'.

you also have to define 1 = 0', and 2 = 1'. then the proof of the

theorem above is a little different:

proof: use the second part of the definition of + first:

      1 + 1 = (1 + 0)'

      now use the first part of the definition of + on the sum in

      parentheses:   1 + 1 = (1)' = 1' = 2   q.e.d.