What is the slope intercept equation of the line that contains the point (0,3) and (4,7)?

Question

What is the slope intercept equation of the line that contains the point (0,3) and (4,7)?

Answer 1

Hi Drea--

 

The cool part here is that you already know your "b," or y-intercept, because 0,3 is right on the y axis at 3.

 

So: so far you have y = mx + 3

 

To figure out m (which is the slope) take the 2 y values and subtract them, one from the other. Let's do 7 - 3, which equals 4.

 

Place that 4 in the numerator of a fraction. The denominator will be the difference you get when you subtract one of the x's from the other. (Make sure you do them in the same order you subtracted the y's.) So, that's 4-0, which also equals 4.

 

So your slope is 4/4, which simplifies to 1, and that's the m in your equation.

 

So, y = 1x + 3, but when it's just a 1, we don't bother using it, so it's just...

 

y = x + 3.

 

You'll see that this "checks out" with both ordered pairs. If you graph the two points and then draw a line through them extending in either direction, you can then pick any value for x, add 3 to it to get y, and you'll now have another point that will land on your line.

 

Hope this helps!

 

Matt in NY