The line in the equation is 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. Therefore we know the slope is #-4#.
We can now use the point-slope formula to find an equation for the line in the problem. The point-slope formula states: #(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))#
Where #color(blue)(m)# is the slope and #color(red)(((x_1, y_1)))# is a point the line passes through.
Substituting the slope and point from the problem gives:
#(y - color(red)(-18)) = color(blue)(-4)(x - color(red)(4))#
#(y + color(red)(18)) = color(blue)(-4)(x - color(red)(4))#
Or, we can solve for #y# to put the equation in slope-intercept form:
#y + color(red)(18) = (color(blue)(-4) xx x) - (color(blue)(-4) xx color(red)(4))#
#y + color(red)(18) = -4x - (-16)#
#y + color(red)(18) = -4x + 16#
#y + color(red)(18) - 18 = -4x + 16 - 18#
#y + 0 = -4x - 2#
#y = color(red)(-4)x - color(blue)(2)#
