Applications of the Equation of a Line

Understanding the Equation of a Line

The equation of a straight line is fundamental in coordinate geometry and can be used to solve real-life problems. It is usually written in the form:

$$y = mx + c$$

• $m$ is the slope (gradient) of the line.
• $c$ is the y-intercept, where the line crosses the y-axis.

Real-Life Applications

The equation of a line can be applied in various real-life scenarios, such as:

• Economics: To determine cost functions, where the cost depends linearly on the number of items produced.
• Physics: To describe motion, where distance is a linear function of time.
• Construction: To design ramps or roads with a specific incline.

Graphical Solutions

Graphing linear equations helps visualize solutions and understand relationships between variables. Here’s how to graph a line:

1. Identify the y-intercept: Plot the point $(0, c)$ on the y-axis.
2. Use the slope: From the y-intercept, use the slope $m$ to find another point. For example, if $m = 2$, go up 2 units and 1 unit to the right.
3. Draw the line: Connect the points with a straight line extending in both directions.

Example: Graph the Line $y = 2x + 3$

Worked Example