We can use the point-slope formula to solve this problem. The point-slope formula is:
#color(red)(y - y_1 = m(x - x_1))#
Where #m# is the slope, which for this problem is 2/3 and #(x_1, y_1)# is a point on the line, which for this problem is (-2, 5).
Substituting gives:
#y - 5 = 2/3(x - -2)#
#y - 5 = 2/3(x + 2)#
or, solving for #y# to put the equation in slope-intercept for is:
#y - 5 = 2/3x + 2 * 2/3#
#y - 5 = 2/3x + 4/3#
#y - 5 + 5 = 2/3x + 4/3 + 5#
#y - 0 = 2/3x + 4/3 + (3/3 * 5)#
#y = 2/3x + 4/3 + 15/3#
#y = 2/3x + 19/3#
