need linear equation for

x y
1 20
2 17
3 14
4 11

for every increase of 1 in x, y decreeases by 3

this gives us 3x

y=0=23

so, y=23-3x

y = 20, 17, 14, 11

x = 1, 2, 3, 4

change in y--
17 - 20 = -3
14 - 17 = -3
11 - 14 = -3

change in x--
2 - 1 = 1
3 - 2 = 1
4 - 3 = 1

Slope m = y difference/x difference
m = -3/1 = -3

y = mx + b
To find b using point (1,20)
m = -3

20 = -3(1) + b
20 = -3 + b
b = 23

Therefore, the equation is.
y = -3x + 23

To find the linear equation that describes the relationship between the given values of x and y, we can use the method of finding the slope-intercept form of a linear equation (y = mx + b), where m represents the slope and b represents the y-intercept.

Step 1: Find the slope (m):
The slope of a line can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)

Let's use the values from the first two points (1, 20) and (2, 17):
m = (17 - 20) / (2 - 1)
m = -3 / 1
m = -3

Step 2: Find the y-intercept (b):
Now that we have the slope, we can substitute the coordinates of one of the points (let's use the first point) and solve for b:
y = mx + b
20 = -3(1) + b
20 = -3 + b
b = 20 + 3
b = 23

Step 3: Write the linear equation:
Now that we have the slope (m = -3) and the y-intercept (b = 23), we can write the linear equation in slope-intercept form:
y = -3x + 23

Therefore, the linear equation that fits the given values of x and y is y = -3x + 23.