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#
