a We have to write two equations, one for each type of tree. In both cases we will use the slope-intercept form of the equation.
y= mx+ b
The initial height of a spruce tree b_s is equal to 14 inches. Since it grows 4 inches per year the slope of the equation m_s is equal to 4.
y_s= 4x+ 14
We are also told that the initial height of a hemlock tree b_h is equal to 8 inches. It grows 6 inches per year, so the slope of the equation m_h is equal to 6.
y_h= 6x+ 8
Combining the equations, we get a system.
y_s= 4x+ 14 y_h= 6x+ 8
b In order to solve the system by graphing we will draw the lines representing the equations and find the intersection.
We can see from the graph that the lines intersect at (3,26), which is the solution of the system. This means that the trees will be equally tall after 3 years, when they will both be 26 inches.
