To write this equation we can use the point-slope formula.
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 this equation:
#(y - color(red)(6)) = color(blue)(2)(x - color(red)(2))#
We can also solve for #y# to put this equation into the more familiar 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)(2) xx x) - (color(blue)(2) xx color(red)(2))#
#y - color(red)(6) = 2x - 4#
#y - color(red)(6) + 6 = 2x - 4 + 6#
#y - 0 = 2x + 2#
#y = 2x + 2#
