Graphing a Linear Parent Function | Understanding Form, Intercepts, and Slope

Graph of Linear Parent Function

The graph of a linear parent function is a straight line

The graph of a linear parent function is a straight line. In general, a linear function has the form:
y = mx + b
where m represents the slope of the line and b represents the y-intercept (the point where the line crosses the y-axis).

To graph a linear parent function, you need two points on the line. The simplest way to find these points is by using the y-intercept and the slope.

1. Y-Intercept: Start by plotting the y-intercept. If the equation is in the form y = mx + b, the y-intercept is the point (0, b), where b is the value of the y-coordinate when x = 0.

2. Slope: Use the slope to find another point on the line. The slope represents the change in y divided by the change in x. If the slope is a fraction, it can be written as rise over run. The rise is the change in y and the run is the change in x. Start at the y-intercept and use the slope to determine a second point on the line.

3. Connect the two points: Once you have the two points, draw a straight line that passes through both of them. This line represents the graph of the linear parent function.

For example, let’s consider the equation y = 2x + 3.
– The y-intercept is (0, 3), where b = 3.
– To find another point, we can use the slope of 2. Starting from (0, 3), we move 2 units up (rise) and 1 unit to the right (run) to find the point (1, 5).

Plotting these two points and connecting them with a straight line, we have the graph of the linear parent function y = 2x + 3.

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