I believe that knowing how to find the equation of a straight line is an essential skill in mathematics. It is a fundamental concept in algebra used in a variety of fields like physics, engineering, and even business. The most basic form of the equation of a straight line is y = mx + b, where m is the slope and b is the y-intercept.
But how do we find these values when we are given two points on the line? In other words, how do you find the equation of a straight line given two points? You can find the equation of a straight line given two points by determining the slope between the two points, then solving for the y-intercept in the slope-intercept equation y=mx+b.
Read on to explore a step-by-step procedure on how to find the equation of a straight line using two points. If you wonder if you can use ChatGPT to learn Calculus, yes, I wrote a whole discussing how.
Step 1: Finding The Slope of The Line
The slope of a line is the ratio of the vertical change to the horizontal change between two points. To find the slope of a line given two points, we use the slope formula:
m = (y2 – y1) / (x2 – x1).
Let’s say we are given two points, (2, 3) and (4, 7).
Using the formula, we can find the slope of the line: m = (7 – 3) / (4 – 2) = 2. A slope of 2 means that the line rises 2 units for every 1 unit to the right it moves.
Step 2: Find The y-intercept
The y-intercept of a line is defined as the point where the line crosses the y-axis. To find the y-intercept, we can use the point-slope equation of a line, y – y1 = m(x – x1).
We can substitute one of the given points into the equation and solve for b, which is the y-intercept.
Using the point (2, 3) and the slope we just found, we get y – 3 = 2(x – 2). Simplifying the equation gives us y = 2x – 1. Therefore, the y-intercept is -1.
Step 3: Write The Equation of The Line
Now that we have found the slope and the y-intercept, we can write the equation of the line in slope-intercept form as follows: y = mx + b.
Plugging in the values we found, we get y = 2x – 1. This is the equation of the straight line that passes through the points (2, 3) and (4, 7).
Step 4: Check your work
I always encourage my student to double-check their work to ensure that the equation they found is correct. One way to do this is to graph the points and draw the line to see if it passes through both points and has the correct slope and y-intercept.
In our example, when we graph the points (2, 3) and (4, 7), we see that the line passes through both points and has a slope of 2 and a y-intercept of -1, confirming that our equation is correct.
Although we have used examples with whole numbers, it is important to know that the same formula works with any type of number, including decimals and fractions.
Also, remember that if the two points provided are the same, you won’t be able to find the equation of the straight line since the line will be undefined.
If you want to learn more about how to find the equation of a straight line given two points, I encourage you to watch the video below.
What to read next:
- Understanding the Basics of Exponential Functions.
- Finding the Set of Values for Which a Line Does Not Intersect a Curve.
- The Best Color Graphing Calculator for Every Student!
- What is Calculus, and is it easy to learn?
I believe that finding the equation of a straight line is a fundamental concept in algebra and geometry. Using the slope-intercept form or the point-slope form is an easy process that makes it easier to determine unknown points on a straight line.
Follow all the steps outlined in this article, including finding the slope of the line, finding the y-intercept, writing the equation of the line, and then double-checking your work by graphing the points.
Now that you have learned the easiest way to find the equation of a straight line given two points, you can confidently tackle that problem on your next math test.