Coordinate geometry is a branch of mathematics that deals with the study of geometric shapes and figures using a coordinate system. In coordinate geometry, we represent points, lines, and shapes on a coordinate plane, which is a two-dimensional grid consisting of two perpendicular lines, often referred to as the x-axis and y-axis. The point where these axes intersect is called the origin and is typically denoted as (0, 0).
Now, let’s discuss the equation of a line in coordinate geometry:
The equation of a line in the form you mentioned, y = mx + c, is called the slope-intercept form of a line. Let’s break down what each part of this equation represents:
- “y” and “x” are variables: These represent the vertical and horizontal coordinates of any point (x, y) on the line.
- “m” is the slope of the line: The slope (m) represents how steep the line is and determines its direction. It is defined as the change in the vertical coordinate (y) divided by the change in the horizontal coordinate (x) between two points on the line. In other words, the slope is the rise over run. Mathematically, it can be expressed as:m = (change in y) / (change in x)
- “c” is the y-intercept: The y-intercept (c) is the point where the line crosses the y-axis. It represents the value of “y” when “x” is equal to 0. In other words, it’s the y-coordinate of the point where the line intersects the y-axis.
So, when you have the equation y = mx + c:
- “m” tells you how the line slants or tilts.
- “c” tells you where the line crosses the y-axis.
With this information, you can graph the line by plotting the y-intercept (0, c) and then using the slope “m” to determine other points on the line. To find additional points, you can move horizontally by a certain amount (the run) and then move vertically by the corresponding amount (the rise) to maintain the slope.
For example, if you have the equation y = 2x + 3, you know that the line has a slope of 2 (it rises 2 units for every 1 unit it runs to the right) and crosses the y-axis at 3.
w1x + w2y + w0 = 0 Another Equation that Represents a Straight Line
The expression “w1x + w2y + w0 = 0” represents a linear equation in two variables, “x” and “y.” This equation is in the standard form of a two-variable linear equation, where:
- “w1” and “w2” are coefficients that determine the slope of the line.
- “w0” is a constant term.
- “x” and “y” are the variables.

When plotted on a Cartesian coordinate system (x-y plane), this equation represents a straight line. The coefficients “w1” and “w2” determine the slope of the line, while the constant term “w0” influences the line’s position with respect to the origin (0,0).
In this form, the equation can be used to represent a line in various contexts, including linear regression, where “w1” and “w2” represent regression coefficients, and the equation describes the relationship between the independent variables “x” and “y” and the dependent variable.
- “w1x + w2y + w0 = 0” is a linear equation in two variables, “x” and “y,” and it can represent a straight line when plotted on a Cartesian coordinate system. This equation is in the standard form of a two-variable linear equation.
- “y = mx + c” is another equation that represents a straight line, but it is in slope-intercept form. In this form, “m” represents the slope of the line, and “c” represents the y-intercept (the point where the line crosses the y-axis).
So, both equations can describe straight lines, but they are written in different forms. The first equation is in standard form, while the second equation is in slope-intercept form.
I hope this explanation helps you understand the basics of the equation of a line in coordinate geometry! If you have any more questions or need further clarification, please feel free to ask.