We can use the point-slope formula to find this equation. 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 values from the problem gives:
#(y - color(red)(-6)) = color(blue)(-1)(x - color(red)(1))#
#(y + color(red)(6)) = color(blue)(-1)(x - color(red)(1))#
Or 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)(6) = (color(blue)(-1) xx x) - (color(blue)(-1) xx color(red)(1))#
#y + color(red)(6) = -x + 1#
#y + color(red)(6) - 6 = -x + 1 - 6#
#y + 0 = -x - 5#
#y = color(red)(-1)x - color(blue)(5)#
