Linear Function Graph
A linear function graph represents a straight line on a coordinate plane
A linear function graph represents a straight line on a coordinate plane. It is defined by the equation y = mx + b, where m is the slope of the line, and b is the y-intercept.
To graph a linear function, follow these steps:
1. Determine the slope (m) and intercept (b) values from the given equation. The slope represents the rate of change of y with respect to x, and the intercept represents the y-value when x is equal to zero.
2. Plot the y-intercept on the y-axis. The y-intercept is the point (0, b), where b is the y-intercept value determined in step 1.
3. Use the slope to find additional points on the line. The slope indicates the relationship between the change in y and the change in x. For example, if the slope is 2, for every 1 unit increase in x, y increases by 2 units. To find points on the line, choose other x-values and calculate their corresponding y-values using the slope.
4. Plot the additional points on the graph.
5. Connect the plotted points with a straight line. Make sure that the line extends beyond the points in both directions.
Note: If the slope is positive, the line rises from left to right. If the slope is negative, the line falls from left to right. If the slope is zero, the line is horizontal. If the slope is undefined, the line is vertical.
For example, let’s graph the linear function y = 2x + 3:
1. The slope is 2 and the y-intercept is 3.
2. Plot the y-intercept at (0, 3).
3. Choose an x-value, say x = 1, and find the corresponding y-value. Using the equation, substitute x = 1: y = 2(1) + 3 = 5. So, another point is (1, 5).
4. Choose another x-value, say x = -1, and find the corresponding y-value. Using the equation, substitute x = -1: y = 2(-1) + 3 = 1. So, another point is (-1, 1).
5. Plot the points (1, 5) and (-1, 1).
6. Connect the points with a straight line.
The graph of the linear function y = 2x + 3 will be a straight line that rises from left to right, intersecting the y-axis at (0, 3).
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