First, we need to determine the slope. The formula for slope is:

#color(red)(m = (y_2 - y_1)/(x_2 - x_1))#

Where #m# is the slope and #(x_1, y_1)# and #(x_2, y_2)# are the points given. Substituting the points we are given for the problem we get the slope as:

#m = (-4 - 7)/(-3 - 2)#

#m = (-11)/(-5)#

#m = 11/5#

Now that we have the slope we can use the point-slope formula to get the equation for the line. This formula is:

#color(red)((y - y_1) = m(x - x_1))#

Where #m# is the slope and #(x_1, y_1)# are a given point. Substituting the slope we calculated and one of the points gives:

#y - -4 = 11/5(x - -3)#

#y + 4 = 11/5(x + 3)#

We can now solve for #y# to get the slope-intercept form while keeping the equation balanced:

#y + 4 = 11/5x + 33/5#

#y + 4 - 4 = 11/5x + 33/5 - 4#

#y + 0 = 11/5x + 33/5 - (5/5)*4#

#y = 11/5x + 33/5 - 20/5#

#y = 11/5x + 13/5#