# y= mx + c

## y= mx + c

- “y = mx + c” is the equation of a straight line in a 2D space or on a cartesian plane.
- This line is termed as a linear function because the power of its variable x is 1.
- In the equation, ‘m’ represents the slope or gradient of the line. This helps determine the steepness of the line.
- The ‘m’ value can be positive, negative, or zero, each scenario altering the direction and steepness of the line.
- A positive ‘m’ value means the line rises from left to right, negative ‘m’ value suggests the line falls from left to right, while a zero ‘m’ value results in a horizontal line.
- The ‘c’ in the equation is known as the y-intercept. This is where the line intercepts or crosses the y-axis on the cartesian plane.
- The y-intercept, ‘c’, does not affect the slope of the line but simply moves it up or down depending upon its value.
- If ‘c’ is positive, the line crosses the y-axis above the origin, but if ‘c’ is negative, the line crosses the y-axis below the origin.
- The equation “y = mx + c” can be rewritten into different forms to provide more information about the line’s properties, such as point-slope form or slope-intercept form.
- To plot a line of “y = mx + c”, start at the y-intercept (c), then use the slope (m) to find other points. For a positive slope, move up and to the right. For a negative slope, move down and to the right.
- To determine the slope ‘m’ between two given points (x1, y1) and (x2, y2) on the line, use the formula m = (y2 - y1) / (x2 - x1).
- Familiarity with “y = mx + c” is not only beneficial for understanding basic linear functions but is also crucial for advanced topics such as calculus, matrices, and linear algebra.