The slope-intercept form of a linear equation is: #y = color(red)(m)x + color(blue)(b)#

Where #color(red)(m)# is the slope and #color(blue)(b)# is the y-intercept value.

We can substitute the slope and values for the point from the problem for #m#, #x# and #y# in the formula and solve for #b#:

#7 = (color(red)(-1/3) * -4) + color(blue)(b)#

#7 = 4/3 + color(blue)(b)#

#7 - color(red)(4/3) = 4/3 - color(red)(4/3) + color(blue)(b)#

#(3/3 * 7) - color(red)(4/3) = 0 + color(blue)(b)#

#21/3 - color(red)(4/3) = color(blue)(b)#

#17/3 = color(blue)(b)#

We can now substitute the slope given in the problem and the value for #b# we calculated into the slope-intercept formula to find the equation to solve the problem:

#y = color(red)(-1/3)x + color(blue)(17/3)#