We can use the point-slope formula to find the equation of the line meeting the criteria 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 values for the point from the problem gives:
#(y - color(red)(16)) = color(blue)(-13/5)(x - color(red)(-23))#
#(y - color(red)(16)) = color(blue)(-13/5)(x + color(red)(23))#
We can also solve for #y# to find 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)(16) = (color(blue)(-13/5) xx x) + (color(blue)(-13/5) xx color(red)(23))#
#y - color(red)(16) = -13/5x - 299/5#
#y - color(red)(16) + 16 = -13/5x - 299/5 + 16#
#y - 0 = -13/5x - 299/5 + (16 xx 5/5)#
#y = -13/5x - 299/5 + 80/5#
#y = color(red)(-13/5)x - color(blue)(219/5)#
