We can use the point-slope formula to write an 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 information from the problem gives:
#(y - color(red)(21/10)) = color(blue)(8/25)(x - color(red)(41/5))#
We can solve for #y# to convert to 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)(21/10) = (color(blue)(8/25) xx x) - (color(blue)(8/25) xx color(red)(41/5))#
#y - color(red)(21/10) = 8/25x - 328/125#
#y - color(red)(21/10) + 21/10 = 8/25x - 328/125 + 21/10#
#y - 0 = 8/25x - (2/2 xx 328/125) + (25/25 xx 21/10)#
#y = 8/25x - 656/250 + 525/250#
#y = 8/25x - 131/250#
