Finding the Equation of a Straight Line
The equation of a straight line is y = mx + c. The gradient m shows how steep the line is, found from two points using m = (y₂ − y₁) ÷ (x₂ − x₁). The y-intercept c is where the line crosses the y-axis, when x = 0.
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The Straight Line Formula: y = mx + c
- m is the gradient and tells you how steep the line is.
- c is the y-intercept and shows where the line crosses the y-axis.
Finding a Linear Equation Using Two Points
- The gradient is found using ₂ − y₁) ÷ (x₂ − x₁).
- For example, with points (2,3) and (4,7), the gradient is .
Checking If a Point Lies on a Line
- Substitute (3,5) into to check if .
- Because , the point lies on the line.
Practice Questions
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What does the y-intercept (c) represent in the equation ?
Correct! 🎉 +10 pointsNot quite right
The y-intercept (c) is the point where the line crosses the y-axis, i.e., when . The slope (m) represents how steep the line is.
What is the formula for calculating the slope (m) of a line?
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The formula for the slope (m) is the change in y divided by the change in x. This gives us the steepness of the line.
Given the equation , does the point (−2, −4) lie on the line?
Correct! 🎉 +20 pointsNot quite right
When we substitute into the equation , we get , which does not match the given y-coordinate of −4. Therefore, the point does not lie on the line.
Given the points (2, 3) and (4, 7), what is the slope (m) of the line?
Correct! 🎉 +20 pointsNot quite right
The slope is calculated using the formula . For these points, .
What is the equation of the line that passes through the point (0, 5) and (2, 9)?
Correct! 🎉 +20 pointsNot quite right
First calculate the slope using . Since the line passes through (0, 5), the y-intercept (c) is 5. Thus, the equation is .
What is the equation of the line that passes through the points (1, 2) and (3, 8)?
Correct! 🎉 +30 pointsNot quite right
First, calculate the slope using . Next, use the point (1, 2) and the equation to find the y-intercept: , so . Therefore, the equation of the line is .
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Interactive Activity
Finding the equation of a straight line using 2 points
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Students Also Ask
The questions students bump into most on this topic
The formula is y = mx + c. Here, m is the gradient, which measures how steep the line is. The y-intercept c is where the line crosses the y-axis. Once you know m and c, the equation describes every point on the line.
In y = mx + c, m is the gradient and c is the y-intercept. The gradient tells you how steep the line is. You find it from the change in y divided by the change in x. The y-intercept is the value of y where the line crosses the y-axis.
No, it does not matter. You can assign either point as P1 and the other as P2. Just keep the same order when you work out the change in y and the change in x. Then the gradient, and the final equation, come out the same.
If you already know where the line crosses the y-axis, c is simply that value. At the y-intercept the line meets the y-axis, where x equals 0 and y equals c. So you can read c straight off without any calculation.
Substitute the point's x and y values into the equation of the line. If both sides are equal, the point lies on the line. For example, put (3, 5) into y = 2x - 1. This gives 5 = 5, so (3, 5) lies on the line. But (-2, -4) gives -4 = -5, so it does not.