Write the equation of the line, in standard form, that has a y-intercept of 2 and is parallel to 2x + y = -5. Include your work in your final answer. Can someone please explain how to do this?

Question

anonymous · Answer

Let's rearrange the equation given to us in a nice form:$$y=-2x-5$$What does it mean for two linear slopes to be parallel? They must have the same slope! So immediately we can begin to write our equation as$$y=-2x$$Next it tells us that the y-intercept is 2, which means it intercepts the y-axis at y=2. Adding this to our equation, we get$$y=-2x+2$$Let's check and see if this is ok! If we plug in 0, we see that$$x=0:~~~~~y=-2(0)+2=2$$Which is where it will intercept the y-axis!