The point-slope form of a linear equation is: #(y - color(blue)(y_1)) = color(red)(m)(x - color(blue)(x_1))#
Where #(color(blue)(x_1), color(blue)(y_1))# is a point on the line and #color(red)(m)# is the slope.
Substituting the values from the point and slope in the problem gives:
#(y - color(blue)(-5)) = color(red)(-3/2)(x - color(blue)(-4))#
#(y + color(blue)(5)) = color(red)(-3/2)(x + color(blue)(4))#
We can also solve for #y# to put the equation in slope-intercept form. 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.
#y + color(blue)(5) = (color(red)(-3/2) xx x) + (color(red)(-3/2) xx color(blue)(4))#
#y + color(blue)(5) = color(red)(-3/2)x + (-12/2)#
#y + color(blue)(5) = color(red)(-3/2)x + (-6)#
#y + color(blue)(5) = color(red)(-3/2)x - 6#
#y + color(blue)(5) - 5 = color(red)(-3/2)x - 6 - 5#
#y + 0 = color(red)(-3/2)x - 11#
#y = color(red)(-3/2)x - color(blue)(11)#
