I am not great at equations... I keep practicing and working these problems and questions out but I always seem to get different answers can someone please guide me on how or tell me the correct way to work these problems out>>

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?

My answer is = year 2000

b)What x-value represents the year 2018?

x= 22

c)What is the slope (or rate of change) of this equation?

How or where do I start on this one??

d)What is the y-intercept?

e)What does the y-intercept represent?

f)Assuming this growth trend continues, what will the price of gasoline be in the year 2018? How did you arrive at your answer?

Answered above.

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To find the answers to the questions regarding the linear equation, let's break down each question:

a) What year would be represented by x = 4?

To find the year represented by x = 4, you need to substitute the value of x, which is 4, into the equation and solve for y. The equation is:

y = 0.15x + 0.79

Substituting x = 4:

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

Therefore, the year represented by x = 4 is 1997 + 4 = 2001.

b) What x-value represents the year 2018?

To find the x-value representing the year 2018, you need to know that x represents the number of years after 1997. So, finding x would involve calculating the difference between 2018 and 1997:

x = 2018 - 1997
x = 21

Therefore, the x-value representing the year 2018 is 21.

c) What is the slope (or rate of change) of this equation?

The slope of a linear equation is the coefficient of the x-term. In this case, the equation is:

y = 0.15x + 0.79

The slope, represented by the coefficient 0.15, indicates the rate at which y changes with respect to x. It represents the average increase in y for every unit increase in x. In this equation, the slope is 0.15.

d) What is the y-intercept?

The y-intercept is the value of y when x is equal to 0. In this equation:

y = 0.15x + 0.79

When x is 0, the equation becomes:

y = 0.15(0) + 0.79
y = 0 + 0.79
y = 0.79

Therefore, the y-intercept is 0.79.

e) What does the y-intercept represent?

The y-intercept represents the starting point of the equation, or the value of y when x is 0. In this context, it would represent the estimated average cost of gas in the starting year of 1997.

f) Assuming this growth trend continues, what will the price of gasoline be in the year 2018? How did you arrive at your answer?

To estimate the price of gasoline in the year 2018, you need to substitute x = 21 into the equation and solve for y:

y = 0.15x + 0.79
y = 0.15(21) + 0.79
y = 3.15 + 0.79
y = 3.94

Therefore, assuming the growth trend continues, the estimated average cost of gas in the year 2018 would be $3.94.