So, of course, this may be confused by the lines of communication, but assuming I understand the problem and got the right X and Y, I come up with a model that looks like yours:
##
## Call:
## lm(formula = dat$Year ~ dat$MonthMean)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.654 -2.274 0.641 4.124 7.718
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1980.54 2.39 828.81 < 2e-16 ***
## dat$MonthMean 10.12 1.39 7.29 6.1e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.26 on 28 degrees of freedom
## Multiple R-squared: 0.655, Adjusted R-squared: 0.643
## F-statistic: 53.2 on 1 and 28 DF, p-value: 6.1e-08
##
Which could be plotted as
And the only thing I see different from yours is you seem to have your Y and X axes reversed, so you have a plot that reflects the true plot about the y=x line. So I would suggest Y=Year on the up and down / Y axis and X=Mean Price per Gallon on the right/left X-axis.
Additionally, I see an equation on your graph that says \[ y=.0648x -127.74 \] whereas the equation of the regression line should be \[ y=1980.54 + 10.123x \] (which you can find from the output from your regression) Perhaps this is a result of your axes switch?
Hey is that what you needed?