Question 190802
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The line <font color=blue>y=0.15x+0.79</font> (EQN 1) represents an estimate of the average cost of gasoline for each year. The line <font color=blue>0.11x-y=-0.85</font> (EQN 2 ) estimates the price of gasoline in January of each year (Bureau of Labor Statistics, 2006). 



* Just by looking on the Line Eqns., the 2 lines are neither parallel nor perpendicular - because of the Slope. 
If they intersect, we'll see:


EQN 1, {{{y=0.15x+0.79}}} :
Let fy=0:
{{{0=0.15x+0.79}}}
{{{0.15x=-0.79}}} ---> {{{cross(0.15)x/cross(0.15)=cross(-0.79)5.27/cross(0.15)}}}
{{{red(x=-5.27)}}} X-Intercept


Let fx=o:
{{{y=0.15(0)+0.79}}}
{{{red(y=0.79)}}} Y-Intercept



EQN 2: {{{0.11x-y=-0.85}}}
Let fy=0:
{{{0.11(x)-0=-0.85}}}
{{{cross(0.11)x/cross(0.11)=cross(-0.85)7.73/cross(0.11)}}}
{{{red(x=-7.73)}}}, X-Interecpt


Let fx=0:
{{{0.11(0)-y=-0.85}}}
{{{red(y=0.85)}}}, Y-Intercept


We'll see the graph:
{{{drawing(500,500,-10,8,-2,2,graph(500,500,-10,8,-2,2,0.15x+0.79,0.11x+0.85),blue(circle(-5.27,0,.12)),blue(circle(0,0.79,0.12)),blue(circle(-7.73,0,.12)),blue(circle(0,0.85,.12)))}}} ----> {{{red(RED=EQN1)}}}; {{{green(GREEN=EQN2)}}}



Now, as we see the 2 lines intersect, and we calculate the exact point.


Substitute EQN 1 to EQN 2:

{{{0.11x-highlight(0.15x+0.79 )=-0.85}}}
{{{0.11x-0.15x-0.79=-0.85}}}
{{{-0.04x=-0.85+0.79=-0.06}}}
{{{cross(-0.04)x/cross(-0.04)=cross(-0.06)1.5/cross(-0.04)}}}
{{{red(x=1.5)}}}


Also, substitute {{{x=1.5}}} to EQN 1:
{{{y=0.15(1.5)+0.79=0.225+0.79}}}
{{{red(y=1.015)}}}


*The two lines intersect at point <font color=blue>(1.5,1.015)</font>



Thank you,
Jojo</font>