The linear equation

y=0.15x+0.79

represents an estimate of the average cost of gas for year x starting in 1997. the year 1997 would be represented by x=1, for example, as it is the first year in the study. similarly, 2005 would be year 9, or x=9

A) what year would be represented by x=4?

B) what x-value represent the year 20018?

C) what is the slope (or rate of change) of this equation?

D) what is the y-intercept?

A) If the year 1997 is year x=1, then 1996 is year x = 0.

Add 4 to 1996 to get year x = 4

1996 + 4 = 2000

B) I assume you mean 2018. Subtract 1996, which is year x = 0

2018 - 1996 = 22

So 2018 is year x = 22

C,D) The equation is in the form y = mx + b.

y = 0.l5 x + 0.79
y = mx + b
m = 0.15
b = 0.79

m is the slope, and b is the y intercept.

What year would be represented by x=4

To answer these questions, let's analyze the given linear equation:

y = 0.15x + 0.79

A) To find the year represented by x = 4, we need to substitute x=4 into the equation and solve for y:

y = 0.15(4) + 0.79
y = 0.6 + 0.79
y = 1.39

Therefore, x=4 would represent the year 1997 + 4 = 2001.

B) To find the x-value that represents the year 20018, we need to solve the equation for x when y = 20018:

20018 = 0.15x + 0.79
19917.21=0.15x
x = 19917.21 / 0.15

Using division, we find that x ≈ 132,781.4.

Therefore, the x-value that represents the year 20018 would be approximately 132,781.

C) The slope (or rate of change) of the equation is the coefficient of x, which is 0.15. This means that for every increase of 1 unit in x, y increases by 0.15.

D) The y-intercept is the value of y when x = 0. In the given equation, it is represented by the constant term, which is 0.79. Therefore, the y-intercept is 0.79.

In summary:
A) x=4 represents the year 2001.
B) The x-value representing the year 20018 is approximately 132,781.
C) The slope (rate of change) of the equation is 0.15.
D) The y-intercept is 0.79.