Linear Function Graph
A linear function represents a straight line on a graph and can be represented by the equation y = mx + b, where m is the slope of the line and b is the y-intercept
A linear function represents a straight line on a graph and can be represented by the equation y = mx + b, where m is the slope of the line and b is the y-intercept. The slope (m) determines how steep the line is, while the y-intercept (b) represents the point where the line intersects the y-axis.
To graph a linear function, you need two points on the line or the slope and y-intercept. Let’s go through an example:
Example: Graph the linear function y = 2x + 3.
1. Slope: In this case, the slope is 2. It tells us that for every increase of 1 in the x-coordinate, the y-coordinate increases by 2. If the slope were negative, the line would be downhill.
2. Y-intercept: The y-intercept for this equation is 3. This is the value of y when x is zero. It gives us the point (0, 3).
3. Plotting points: We can find additional points by using the slope. Let’s choose x = 1. By plugging it into the equation, we get y = 2(1) + 3 = 5. So we have another point (1, 5).
4. Drawing the line: With these two points, we can draw a straight line through them. The line should be straight because it is a linear function.
5. Extending the line: If you want, you can extend the line beyond the plotted points to visualize the behavior of the function for other values of x.
So in this case, the graph of the linear function y = 2x + 3 is a straight line that passes through the points (0, 3) and (1, 5), and it continues in both directions.
Remember, the graph of a linear function will always be a straight line, and you can determine its slope and y-intercept from its equation.
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