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 from the problem for #m# and the values from the point in the for #x# and #y#. We can than solve the equation for #color(blue)(b)#.

#y = color(red)(m)x + color(blue)(b)# becomes:

#-20 = (color(red)(-1/2) xx 3) + color(blue)(b)#

#-20 = -3/2 + color(blue)(b)#

#color(red)(3/2) - 20 = color(red)(3/2) - 3/2 + color(blue)(b)#

#color(red)(3/2) - (2/2 xx 20) = 0 + color(blue)(b)#

#color(red)(3/2) - 40/2 = color(blue)(b)#

#-37/2 = color(blue)(b)#

Substituting the slope from the problem and the value for #color(blue)(b)# we calculated into the formula gives:

#y = color(red)(-1/2)x + color(blue)(-37/2)#

#y = color(red)(-1/2)x - color(blue)(37/2)#