We can use the point-slope formula to write and equation for this line. 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)(-6)) = color(blue)(6/7)(x - color(red)(6))#
#(y + color(red)(6)) = color(blue)(6/7)(x - color(red)(6))#
If necessary, 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)(6/7) * x) - (color(blue)(6/7) * color(red)(6))#
#y + color(red)(6) = 6/7x - 36/7#
#y + color(red)(6) - 6 = 6/7x - 36/7 - 6#
#y + 0 = 6/7x - 36/7 - (7/7 xx 6)#
#y = 6/7x - 36/7 - 42/7#
#y = color(red)(6/7)x - color(blue)(78/7)#
