We can use the point-slope formula to find the equation of the 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)(1)(x - color(red)(4))#
#(y + color(red)(6)) = color(blue)(1)(x - color(red)(4))#
If necessary, we can convert this equation to slope-intercept by solving for #y#. 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) = x - color(red)(4)#
#y + color(red)(6) - 6 = x - color(red)(4) - 6#
#y + 0 = x - 10#
#y = color(red)(1)x - color(blue)(10)#
