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)(14/7)) = color(blue)(-3/49)(x - color(red)(17/7))#
#(y - color(red)(2)) = color(blue)(-3/49)(x - color(red)(17/7))#
We can convert this formula to the slope-intercept form 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)(2) = (color(blue)(-3/49)xxx) - (color(blue)(-3/49)xxcolor(red)(17/7))#
#y - color(red)(2) = -3/49x - (-51/343)#
#y - color(red)(2) = -3/49x + 51/343#
#y - color(red)(2) + 2 = -3/49x + 51/343 + 2#
#y - 0 = -3/49x + 51/343 + (2 xx 343/343)#
#y = -3/49x + 51/343 + 686/343#
#y = color(red)(-3/49)x + color(blue)(737/343)#
