Work out linear equations easily from two points

TL;DR

Learn how to find the equation of a linear graph using two given points, using the formula y = mx + b.

Transcript

good day welcome to Tech math Channel what we're going to be having a look at in this video is linear equations that is equations that if we were to graph them give nice straight lines like this one here specifically in this video what we're going to have a look at is how to work out the equation for this particular type of graph knowing only two p... Read More

Key Insights

• 🫥 Linear equations represent graphs that are straight lines.
• 😃 The formula for a linear equation is y = mx + b, where m represents the gradient and b represents the y-intercept.
• 💱 The gradient is found by calculating the rise over the run, which measures the change in y divided by the change in x.
• 😥 Two points on a linear graph can be used to find the equation by calculating the gradient and substituting one point into the equation to solve for the y-intercept.
• 😀 The y-intercept is the point where the graph intersects the y-axis.
• 📈 Positive and negative gradients indicate whether the graph slopes upward or downward, respectively.
• 😥 The equation of a linear graph can be verified by substituting the values of the given points into the equation.

Questions & Answers

Q: How do you find the equation of a linear graph using two given points?

To find the equation, calculate the gradient (m) by finding the change in y divided by the change in x. Then substitute one of the points into the equation y = mx + b to solve for b, the y-intercept.

Q: What does the gradient of a linear graph represent?

The gradient (m) represents the rate at which the graph is sloping or tilting. It measures how far the graph rises (or falls) for every unit increase in the x-coordinate.

Q: Can you provide an example of finding the equation of a linear graph?

Sure! Let's say we have two points: (1, 3) and (3, 5). We calculate the gradient as (5-3)/(3-1) = 1. Then, substituting (1, 3) into y = mx + b, we solve for b as follows: 3 = 1(1) + b, which gives us b = 2. Therefore, the equation is y = x + 2.

Q: What if the gradient is negative in a linear equation?

A negative gradient means the graph is sloping downward from left to right. The calculation process remains the same, but the resulting equation will have a negative coefficient for x.

Summary & Key Takeaways

• Linear equations can be represented by straight-line graphs and described by the equation y = mx + b.

• To find the equation of a linear graph, we need two points on the line and calculate the gradient (m) and the y-intercept (b).

• The gradient is calculated as the rise over the run, which represents the change in y divided by the change in x.