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Liger20
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Hello, could someone please explain to me why the equation y=mx+b uses 'm' for slope and 'b' for y-intercept? This has always bothered me for some reason.
Liger20 said:Hello, could someone please explain to me why the equation y=mx+b uses 'm' for slope and 'b' for y-intercept? This has always bothered me for some reason.
The equation y=mx+b is known as the slope-intercept form of a linear equation. It represents a line on a graph and helps us understand how the value of y changes in relation to the value of x. The letter m represents the slope or steepness of the line, while b represents the y-intercept, which is the point where the line crosses the y-axis.
The slope of a line can be calculated by dividing the change in y-values (vertical change) by the change in x-values (horizontal change) of any two points on the line. This can also be represented as (y2-y1)/(x2-x1), where (x1,y1) and (x2,y2) are two points on the line. In the equation y=mx+b, the value of m represents the slope of the line.
The y-intercept is the point at which the line crosses the y-axis. In the equation y=mx+b, the value of b represents the y-coordinate of the y-intercept. It tells us the starting value of y when x is equal to 0, and helps us understand the position of the line on the y-axis.
Yes, the slope and y-intercept can have negative values. A negative slope means that the line is decreasing from left to right, while a negative y-intercept means that the line crosses the y-axis below the origin (0,0). This can be seen in equations such as y=-2x+5, where the slope is -2 and the y-intercept is 5.
The slope and y-intercept have a significant impact on the graph of a line. The slope determines the steepness of the line, with a larger slope resulting in a steeper line. The y-intercept determines the position of the line on the y-axis, with a higher y-intercept resulting in a line that is higher on the y-axis. Together, the slope and y-intercept help us understand the direction, steepness, and position of a line on a graph.