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 values from the point in the problem gives:
#(y - color(red)(5)) = color(blue)(-1)(x - color(red)(1))#
We can 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(red)(5) = (color(blue)(-1) xx x) - (color(blue)(-1) xx color(red)(1))#
#y - color(red)(5) = -1x - (-1)#
#y - color(red)(5) = -1x + 1#
#y - color(red)(5) + 5 = -1x + 1 + 5#
#y - 0 = -1x + 6#
#y = color(red)(-1)x + color(blue)(6)#
