First, we can write an equation in point-slope form. 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 point from the problem gives:
#(y - color(red)(-1)) = color(blue)(-1/4)(x - color(red)(8))#
#(y + color(red)(1)) = color(blue)(-1/4)(x - color(red)(8))#
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.
We can now solve the point-slope form of the equation for #y# to put it in slope-intercept form.
#y + color(red)(1) = (color(blue)(-1/4) xx x) - (color(blue)(-1/4) xx color(red)(8))#
#y + color(red)(1) = -1/4x - (-8/4)#
#y + color(red)(1) = -1/4x + 2#
#y + color(red)(1) - 1 = -1/4x + 2 - 1#
#y + 0 = -1/4x + 1#
#y = color(red)(-1/4)x + color(blue)(1)#
