Slope Intercept Form
The slope-intercept form is a way to represent a linear equation in the form of y = mx + b, where m represents the slope and b represents the y-intercept
The slope-intercept form is a way to represent a linear equation in the form of y = mx + b, where m represents the slope and b represents the y-intercept.
To understand the slope-intercept form, let’s break it down:
y: This represents the dependent variable or the output variable. It is the variable we are trying to solve for.
x: This represents the independent variable or the input variable. It is the variable we have control over or can manipulate.
m: This represents the slope of the line. Slope measures the steepness or incline of a line. It refers to how much the y-coordinate changes for every unit change in the x-coordinate. A positive slope means the line is going uphill from left to right, while a negative slope means the line is going downhill.
b: This represents the y-intercept of the line. The y-intercept is the point where the line crosses or intersects the y-axis. It indicates the value of y when x is equal to zero.
Using the slope-intercept form, you can easily identify the slope and y-intercept of a linear equation. The slope, m, reveals the rate of change of the line, while the y-intercept, b, gives you the starting value of y.
For example, let’s consider the equation y = 2x + 3.
In this equation, the slope, m, is 2. This means that for every unit increase in x, y will increase by 2. Therefore, the line is going up 2 units for every 1 unit it moves to the right.
The y-intercept, b, is 3. This tells us that when x is equal to zero (or the line intersects the y-axis), y is equal to 3. This is the starting point of the line.
By using the slope-intercept form, you can easily graph the linear equation by plotting the y-intercept (0, b) and using the slope to determine additional points on the line.
In summary, the slope-intercept form (y = mx + b) provides a simple and convenient way to express linear equations, allowing you to quickly identify the slope and y-intercept and easily graph the equation.
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