To solve the equation [tex]\( e^{4 - 3x} = \frac{4}{3} x + 9 \)[/tex] by graphing, we need to graph the individual components of the equation and find their intersection points. Specifically, we will graph the following equations:
1. [tex]\( y = \frac{4}{3} x + 9 \)[/tex] — This is a linear equation representing the right-hand side of the original equation.
2. [tex]\( y = e^{4 - 3x} \)[/tex] — This is an exponential equation representing the left-hand side of the original equation.
By graphing these two equations on the same coordinate plane, the solutions to the original equation [tex]\( e^{4 - 3x} = \frac{4}{3} x + 9 \)[/tex] are where these graphs intersect.
So, the equations that should be graphed are:
[tex]\[ y = \frac{4}{3} x + 9 \][/tex]
[tex]\[ y = e^{4 - 3x} \][/tex]
These graphs will intersect at points whose [tex]\( x \)[/tex]-coordinates are the solutions to the equation [tex]\( e^{4 - 3x} = \frac{4}{3} x + 9 \)[/tex].
