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.