could someone please evaluate what i have so far and help me with the last few questions...
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. similarily, 2005 would be year 9, or x=9.
a) what year would be represented by x = 4? 2000
b) what x-value represents the year 2018? 22
c) what is the slope (or rate of change) of thsi equation?
2018: 0.15(22) + 0.79 = $4.09
1997: $0.94
4.09–0.94 divided by 2018-1997
= 3.15 divided by 21
= 0.15
= answer is $0.15 per year
d) what is the y-intercept? no idea
e) what does the y-intercept represent? where the line crosses on the graph
f) assuming this growth trend continues, what will the price of gas be in 2018? how did you arrive at thsi answer?
2018: 0.15(22) + 0.79 = $4.09
1997: 0.15(1) + 0.79 = $0.94
4.09–0.94 divided by 2018-1997
= 3.15 divided by 21
= 0.15 = $0.15 per year
a, b and c are correct.
d) The y-intersept (where x = 0) is y = 0.79
e) The x-intercept (where y = 0) is
x = -0.79/0.15 = -5.267
f) $4.09 is correct. Your other calculations are unnecessary
To evaluate the given linear equation and answer the remaining questions:
a) To find the year represented by x = 4, you simply substitute x = 4 into the equation: y = 0.15x + 0.79. Therefore, when x = 4, the year represented is 1997 + 4 = 2000.
b) To find the x-value that represents the year 2018, you need to solve the equation y = 0.15x + 0.79 for x. Set y = 2018 and solve for x:
2018 = 0.15x + 0.79
Subtract 0.79 from both sides:
2018 - 0.79 = 0.15x
1237.21 = 0.15x
Divide both sides by 0.15:
x ≈ 822.14
Since x represents the number of years since 1997, you need to add 822.14 to 1997 to get the year 2018. Therefore, x = 822.14 + 1997 = 2019.14, which can be rounded to 2019 or approximated as 22.
c) The slope of the equation represents the rate of change. In this case, the slope is 0.15, which means that for every one unit increase in x (year), the corresponding y (average cost of gas) increases by 0.15 units. Therefore, the slope is $0.15 per year.
d) To find the y-intercept, you set x = 0 in the equation y = 0.15x + 0.79:
y = 0.15(0) + 0.79
y = 0 + 0.79
y = 0.79
Therefore, the y-intercept is 0.79.
e) The y-intercept represents the point where the line crosses the y-axis on a graph. In this context, it represents the estimated average cost of gas in the year 1997.
f) To find the estimated price of gas in 2018, you substitute x = 22 into the equation y = 0.15x + 0.79:
y = 0.15(22) + 0.79
y ≈ 3.3 + 0.79
y ≈ 4.09
Therefore, based on the given equation and assuming the growth trend continues, the estimated price of gas in 2018 would be approximately $4.09.