Question

What is the equation of the line that passes through the points (0, 6) and (-3, 0) and is parallel to y = 2x + 5

Answer 1

y = 2x + 6

Explanation:

The equation for this is y=mx+b, m being for slope and b being the y-intercept.

The first and easiest way to figure out this first is by finding the slope. Now because you have the information that it needs to be parallel, it's very fast and simple. Parallel means that it has the same slope and the lines will never cross each other. So, since the slope for this is 2, the new line you will be making will also have a slope of 2.

EXTRA NOTE- if it were perpendicular, you'd want to do the opposite reciprocal. Instead of being 2, it'd be -1/2, but luckily we're just dealing with parallel.

Now we need to find what the y-intercept is. Since math basically has a formula for everything, you will be using y-y(1)= m(x-x(1)). Now that looks slightly confusing, but basically you will just plug your y value into the y(1) and x coordinate into x(1) to simplify into slope intercept form (don't forget your slope!). It's always easier to use positive numbers for this, so I'll be using the coordinates (0, 6) and plug it in.

REMEMBER- coordinates are (x, y). Don't get it mixed up!

1. Write out your equation: y - 6 = 2 ( x - 0 )

2. Distribute: y - 6 = 2x - 0

3. Add 6 to the other side to get into your slope intercept form: y = 2x + 6

And that's how you get your line. Hope this helped and made at least some sense. :)

Answer 2

y=2x+6

solution:

Alright, since the line is PARALLEL, the slope will remain the same. let call the # we will add to that b (like the 5 in y=2x+5).

so the formula will be y=2x+b

to find be, we will plug in one of the ordered pairs

6=2(0)+b

6=0+b

b=6

So, our equation is y=2x+6

to check:

(-3,0)

0=2(-3)+6

0=-6+6

0=0