Write the equation of a line parallel to the line 2x + 3y = 5 and passes through the point (9, -3)

If you could please tell show me how you got this answer so I can figure out future problems like this thank you.

Question

Write the equation of a line parallel to the line 2x + 3y = 5 and passes through the point (9, -3)

If you could please tell show me how you got this answer so I can figure out future problems like this thank you.

anonymous · Answer

Okay so a line 'parallel' to another means that it has the same gradient. Rearrange the equation you are given so that it is in the standard form for a straight line, which is $$y = mx+c$$. So rearranging $$2x+3y = 5$$$$3y=-2x +5$$$$y=-\frac{ 2 }{ 3 }x+\frac{ 5 }{ 3 }$$So the gradient is -2/3. Now, to work out the equation of a straight line you need the following. $$point (x_{1},y_{1})$$gradient m, the line is givnen by $$y-y_{1} = m(x-x_{1})$$In this case your gradient is -2/3 and the point is (9,-3). Plug this in and we get.$$y+3 = \frac{ -2 }{ 3 }(x-9)$$$$y+3 = \frac{ -2x }{ 3 } + 6$$$$3y+2x= 9$$and that is your final answer. Looks neatest with no fractions in it so we multiply through generally. Hope this helped:)

anonymous · Answer

Thank thank thank so much!!!! I appreciate you very detailed reply!

anonymous · Answer

your*

anonymous · Answer

No problem :) I always think there's no point just giving people the answer, teach a man to fish and all that