Question

Write an equation for the line that is parallel to the given line and that passes through the given point.

y = 5/2x – 10; (–6, –29)

y = -2/5x + 14
y = 5/2x – 14
y = 2/5x– 14
y = 2/5x+133/2

Answer 1

First things first: if a line is parallel to the one given above, then the slope of that line would be the same as this one's. What is the slope of this line?

Answer 2

5/2?

Answer 3

Yes, exactly!

Answer 4

Now, the line will be in the form of this:\[y = \color{blue}{5/2}x + \color{#cc0000}{\rm constant}\]

Answer 5

We just need to find this constant. What do we do? We use the point the above question gives.

Answer 6

So, according to your question, \((-6,-29)\) is a point. What does this mean? This means that when \(x = -6\), you'll have \(y = -29\). Let's plug in these values into\[y = \dfrac{5}{2} x + \rm constant\]

Answer 7

what's the constant?

Answer 8

\[\color{blue}{-29} = \dfrac{5}{2}\left(\color{blue}{-6}\right) + \rm constant \]We are working with that point right now to find the constant, as all the lines with slope 5/2 are in the form \(y = \frac{5}{2}x + \rm constant\)

Answer 9

A constant is just a number, and you can have any number added to the \(x\)-term. This constant here is also known as the "y-intercept", if you have heard of that.

Answer 10

So how do I slove that?

Answer 11

Just get "constant" on one side... just like solving for \(x\)