Equation of a Line Using Point-Slope Formula

Equation of a Line Using Point-Slope Formula

t to find my speed for my point-slope formula. Let's first find the slope. The two points are (2, 5), because at 2 p.m. I was at mile marker 5, and (6, 25) because at 6 p.m. I was at mile marker 25. I can find the slope of this line: delta y / delta x, which is the change in location divided by the change in time. My location has gone from 5 to 25, which is a difference of 20, and time has gone from 2 to 6, which is 4 hours. So, I've gone 20 miles in 4 hours. That gives me 5 mph. I really need to talk to this guy. We're on the freeway here. Why are we going 5 mph? Is there really bad traffic or something? That's neither here nor there. I know my slope now, and I have a point. In fact, I have two points. And I can use either one in point-slope form to find out an equation for where I will be at what time.

This can be simplified to y = 5x - 5.

So point-slope form says that y=y sub 1 + m(x - x sub 1). I'm going to use my current location as my point, so y sub 1 is 25, for mile marker 25, x sub 1 is 6, because it's 6 p.m., and m is my speed, which is a lousy 5 mph. Point-slope form gives me y=25 + 5(x - 6). I can simplify this and I end up with y=5x - 5. Where will I be at 10 p.m.? At 10 p.m., x will be 10. Plug in x=10, and I get 50 - 5, which is y=45. I will be at mile marker 45. That's nowhere close to Vegas. Vegas is at mile marker 100. When will I get to Las Vegas? This means that I need to find what value of x will give me a value of y that's 100. Let's solve 100=5x - 5. I'm going to add 5 to both sides, then divide by 5, and find that x=21 hours after I started. That means I won't get there until 9 a.m. tomorrow. Well, so much for celebrating that wedding. I probably won't even make the after party.

Lesson Summary

Let's recap. To find an equation for the line that goes through point (x sub 1, y sub 1) with some slope m, we use the point-slope formula: y=y sub 1 + m(x - x sub 1). We can use this, for example, to find out where we're going to be at any given point in time on our road trip to Las Vegas.

If, instead of having a point and a slope, we're given two points, we first can calculate the slope and then use point-slope formula. We use this in the case where, for example, I fall asleep on the road to Vegas and I only know the time and our location.