To derive 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 data from the problem gives:
#(y - color(red)(-1/2)) = color(blue)(1/4)(x - color(red)(1))#
#(y + color(red)(1/2)) = color(blue)(1/4)(x - color(red)(1))#
If we want to convert this to slope-intercept form we can solve for #y# as follows:
#y + color(red)(1/2) = color(blue)(1/4)x - (color(blue)(1/4) * color(red)(1))#
#y + color(red)(1/2) = color(blue)(1/4)x - 1/4#
#y + color(red)(1/2) - color(green)(1/2) = color(blue)(1/4)x - 1/4 - color(green)(1/2)#
#y + 0 = color(blue)(1/4)x - 1/4 - (2/2*color(green)(1/2))#
#y = color(blue)(1/4)x - 1/4 - 2/4#
#y = color(blue)(1/4)x - 3/4#
