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

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
2000 is correct. You might make the next part easier by looking at how this was done, instead of just counting up 4.
1996 + 4 = 2000.


b)What x-value represents the year 2018?
1996 + 18 = ??
x= 22

c)What is the slope (or rate of change) of this equation?
The equation for a straight line is
y = mx + b where m is the slope. The equation given is
y=0.15x + 0.79; therefore, 0.15 is the slope.

How or where do I start on this one??

d)What is the y-intercept?
The y intercept is the 0.79 in the original equation. It is the point at which the line crosses the y axis (and x = 0 at that point).
e)What does the y-intercept represent?
See answer above.
f)Assuming this growth trend continues, what will the price of gasoline be in the year 2018? How did you arrive at your answer
Use the equation, plug in x for the number of years (check me out but I think that will be 22) and solve for y.

thank you dr. bob

To solve these problems, you can use the equation provided:

y = 0.15x + 0.79

a) To find the year represented by x = 4, substitute x = 4 into the equation:

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

So, the year represented by x = 4 is 1.39, which is not a valid year representation. However, it seems like you miscalculated. To find the year, you need to add the x value to the base year (1997). Therefore, for x = 4:

Year = 1997 + 4 = 2001

b) To find the x-value representing the year 2018, you need to subtract the base year (1997) from 2018:

x = 2018 - 1997 = 21

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

c) The slope (rate of change) of the equation is represented by the coefficient of x. In this case, the slope is 0.15.

d) The y-intercept is the constant term in the equation, which is 0.79.

e) The y-intercept represents the value of y when x is 0. In this case, it represents the estimated average cost of gas in the base year, which is 1997.

f) To find the estimated average cost of gas in the year 2018, substitute x = 21 into the equation:

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

So, the estimated price of gasoline in the year 2018 would be 3.94.