Please someone help me. I’m struggling so work this out.

Step-by-step explanation:

First of all, look at what the values are in the tables. You are looking to see if the x-values are increasing by 1. Except in problems 5 and 6, that is the case. In those problems, the last x-value is not in sequence. (Not a problem.)

Second, look at the differences between y-values. When the change in x is the same, you want the change in y to be the same. If it s, the rule is a linear rule. (That is the case for all of the problems here.)

Since each rule is a linear rule, it can be written in any of several forms. Your final answer may want to be in "slope-intercept" form, which look__s like ...

  y = mx + b . . . . . . slope-intercept form

To get there, you may want to start with "point-slope" form, which can look like ...

  y = (y2 -y1)(x -x1) +y1 . . . . . . when x2=x1 +1

__

Using this second form on these problems gives ...

(1)  y = (11 -5)(x -1) +5

  y = 6x -1 . . . . . . . . . . . simplified to slope-intercept form

__

(2)  y = (15 -11)(x -2) +11

  y = 4x +3 . . . . . . . . . . . simplified to slope-intercept form

__

(3)  y = (6 -3)(x -3) +3

  y = 3x -6 . . . . . . . . . . . simplified to slope-intercept form

__

(4)  y = (19 -10)(x -2) +10

  y = 9x -8 . . . . . . . . . . . simplified to slope-intercept form

__

(5)  y = (14 -16)(x -(-3)) +16

  y = -2x +10 . . . . . . . . . . . simplified to slope-intercept form

__

(6)  This one is a bit tricky, since the x-values in the table are decreasing, not increasing. One way to deal with that is to reverse the first two table entries, so the first one is (x, y) = (-3, -8) and the second one is (-2, -5). Then our formula gives ...

  y = (-5 -(-8))(x -(-3)) -8

  y = 3x +1 . . . . . . . . . . . simplified to slope-intercept form

Comment on the "point-slope" formula

For arbitrary (x, y) pairs, the "two point" form of the equation of a line is ...

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

In this set of problems, (x2 -x1) = 1 (for all but the last), so we shortened the form to the one we used above:

  y = (y2 -y1)(x -x1) +y1

When the change in x is 1, as for most of these problems, then the change in y is the slope of the line. That is why we called the reduced form here "point-slope" form. It made use of the first point (x1, y1) and the slope (y2 -y1).

This reduced "point-slope" form cannot be used except under the special circumstances that exist for this problem set. (In problem 6, we had to rearrange the problem to create the right circumstances.)

the probability that a bird is green (.30) is true

step-by-step explanation:

c. side angle side. u shares the same sides