Graphing the Linear Parent Function: Understanding the Equation, Slope, and Y-Intercept

Graph of Linear Parent Function

The linear parent function can be written in the form f(x) = mx + b, where m represents the slope and b represents the y-intercept

The linear parent function can be written in the form f(x) = mx + b, where m represents the slope and b represents the y-intercept. This function represents a straight line on a graph.

To graph the linear parent function, we need at least two points. Let’s choose two values for x and find the corresponding y values.

For example, let’s set x = 0. Plugging this into the equation, we have:

f(0) = m(0) + b
f(0) = 0 + b
f(0) = b

So, one point on the graph is (0, b).

Now, let’s choose another value for x, let’s say x = 1. Plugging this into the equation, we have:

f(1) = m(1) + b

At this point, we have two equations with two unknowns (m and b). Let’s say we have the values m = 2 and b = 3.

f(1) = 2(1) + 3
f(1) = 2 + 3
f(1) = 5

So, another point on the graph is (1, 5).

Now we can plot these two points on a coordinate plane and draw a straight line passing through them. The y-intercept point (0, b) represents where the line intersects the y-axis. In this case, it is (0, 3). The second point (1, 5) represents a point on the line’s slope.

The graph of the linear parent function y = 2x + 3 would be a straight line passing through the points (0, 3) and (1, 5).

I hope this explanation helps! If you have any further questions, please let me know.

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