Linear Function Equation
A linear function is a mathematical function that can be represented by a straight line on a graph
A linear function is a mathematical function that can be represented by a straight line on a graph. It has the general form of y = mx + b, where m represents the slope of the line and b represents the y-intercept.
The slope, represented by the variable m, indicates the rate of change of the line. If the value of m is positive, the line will have an upward slope, meaning that y increases as x increases. If m is negative, the line will have a downward slope, indicating that y decreases as x increases.
The y-intercept, represented by the variable b, is the point where the line intersects the y-axis. It represents the value of y when x is equal to zero.
To graph a linear function, you can plot the y-intercept first, and then use the slope to find additional points on the line. To find a second point, you can use the slope to determine how many units to move vertically and horizontally from the y-intercept point. This process can be repeated to find as many points as needed to draw the line.
Example:
Let’s say we have the equation y = 2x + 3.
In this equation, the slope, m, is 2, and the y-intercept, b, is 3.
To graph this equation, we can start by plotting the y-intercept point at (0, 3). Since the y-intercept is at 3, we know that when x is 0, y is 3.
Next, to find another point on the line, we can use the slope. Since the slope is 2, we can move up 2 units and move right 1 unit from the y-intercept point. This gives us another point at (1, 5).
We can continue this process to find more points or draw the line directly by connecting the two points we already have.
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