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frozen [14]
3 years ago
10

determine the intercepts of the line that correspond to the following table of values. -14,9 -10,18 -6,27

Mathematics
1 answer:
Nataliya [291]3 years ago
8 0

I'll need to assume that your "-14,9" means (-14,9); if so, please use parentheses next time to indicate that you're sharing the coordinates of a point.

As we go from (-14,9) to (-10,18), x increases by 4 and y increases by 9.  Thus, the slope of this line is m = rise / run = 9/4.

We want the intercepts of this line.  Let's use the slope-intercept form y = mx + b.  Substituting the given info:  -10 for x and 18 for y, and m = 9/4, we get:

18 = (9/4)(-10) + b, where b is the y-intercept.

Solving for b, we get 18 + 90/4 = (72+90)/4 = 162/4, or 81/2.

Then b = 81/2, and the equation of the line is y = (9/4)x + 81/2.

Now find the x-intercept.  To do this, let y = 0; then (9/4)x = -81/2,  Mult. both sides by 4 to eliminate the fractions:  9x = -162, or x = -18.  The x-intercept is (-18,0) and the y-intercept is (0,81/2)

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1) Ordered pairs are (9,5), (11,8) , (13,11), (15,14)

2) Ordered pairs are (20,20) ,(16,17), (12,14), (8,11)

3) Ordered pairs are     (1,40),(3,22), (7,13), (15,7.5)

Step-by-step explanation:

1) Rule 1: Add 2 starting from 9

Rule 2: Add 3 starting from 5

Sequence 1 is generated using Rule 1 so, it starts with 9 and we add 2 to get the next number.

Sequence 2 is generated using Rule 2 so, it starts with 5 and we add 3 to get the next number.

Sequence 1       Sequence 2       Ordered Pair

9                           5                           (9,5)

11                          8                           (11,8)

13                          11                           (13,11)

15                          14                           (15,14)

2) Rule 1: Subtract 4 starting from 20

Rule 2: Subtract 3 starting from 20

Sequence 1 is generated using Rule 1 so, it starts with 20 and we subtract 4 to get the next number.

Sequence 2 is generated using Rule 2 so, it starts with 20 and we subtract 3 to get the next number.

Sequence 1       Sequence 2       Ordered Pair

20                         20                        (20,20)

16                          17                         (16,17)

12                          14                         (12,14)

8                            11                         (8,11)

3) Rule 1: Multiply by 2 then add 1 starting from 1

Rule 2: Divide by 2 then add 4 starting from 40

Sequence 1 is generated using Rule 1 so, it starts with 1 and then we multiply by 2 and then add 2 to get the next number.

Sequence 2 is generated using Rule 2 so, it starts with 40 and then we multiply by 2 and add 2 to get the next number.

Sequence 1       Sequence 2       Ordered Pair

1                           40                            (1,40)

3                           22                          (3,22)

7                           13                            (7,13)

15                          7.5                           (15,7.5)

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