Fine the equation of the line with the given points

Question

Write an equation of the line containing the given point and parallel to the given line. Express your answer in the form y=mx+b

 

(-8,5); 9x=7y+4

Answer 1

This one isn't too bad so I'll be leaving a lot of the legwork to you.

 

The first thing you probably want to do is convert your equation into y=mx+b form. This gives:

 

y=(9x-4)/7=(⁹/₇)x - ⁴/₇

 

From this you should be able to figure out the slope. (Hint: it's "m")

 

Now the thing that makes lines parallel is the slope. Now that we've extracted that we can move onto the next step.

 

The easiest way to write the equation for a line that passes through a point is called "point-slope form" and it looks like this:

 

y-y₀=m(x-x₀) where x₀ and y₀ are the coordinates of your point.

 

You can test the accuracy of this by plugging one of your coordinate values into the equation to get the other coordinate value. This shows that the line contains the point specified.

 

Then you do some easy algebra to turn it into y=mx+b form and you're done. We know that it is parallel because it has the same slope (m) and that it goes through the point with the double check just above.

 

Good Luck!