Math

QuestionFind xx when y=29y=29 and yy when x=8x=8 based on the pattern in Y=3X+2Y = 3X + 2.

Studdy Solution

STEP 1

Assumptions1. The relationship between xx and yy is linear. The table values are accurate

STEP 2

We need to find the pattern in the table. Let's calculate the difference between consecutive yy values.
Δy=yn+1yn\Delta y = y_{n+1} - y_n

STEP 3

Calculate the difference between consecutive yy values using the given values in the table.
Δy=85=3\Delta y =8 -5 =3Δy=118=3\Delta y =11 -8 =3Δy=1411=3\Delta y =14 -11 =3Δy=1714=3\Delta y =17 -14 =3

STEP 4

We can see that the difference between consecutive yy values is constant and equal to3. This indicates a linear relationship between xx and yy. We can write this relationship asy=mx+by = mx + bwhere mm is the slope (change in yy for a unit change in xx) and bb is the yy-intercept (value of yy when x=0x=0).

STEP 5

We can find the slope mm by dividing the change in yy by the change in xx. Since the change in xx is1 for each step, the slope mm is equal to the change in yy, which is3.
m=Δy/Δx=3/1=3m = \Delta y / \Delta x =3 /1 =3

STEP 6

To find the yy-intercept bb, we can substitute any pair of xx and yy values into the equation and solve for bb. Let's use x=1x=1 and y=5y=5.
5=31+b5 =3 \cdot1 + b

STEP 7

olve the equation for bb.
b=53=2b =5 -3 =2

STEP 8

Now we have the linear equation that describes the relationship between xx and yy.
y=3x+2y =3x +2

STEP 9

We can use this equation to find the value of xx when y=29y=29.
29=3x+229 =3x +2

STEP 10

olve the equation for xx.
x=(292)/3=9x = (29 -2) /3 =9So, when y=29y=29, x=9x=9.

STEP 11

We can also use the equation to find the value of yy when x=8x=8.
y=38+y =3 \cdot8 +

STEP 12

Calculate the value of yy.
y=8+2=26y = \cdot8 +2 =26So, when x=8x=8, y=26y=26.

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