Welcome! Today we are going to explore linear functions—the math behind things that grow at a perfectly steady, predictable pace.
A linear function is like a walking path that goes straight ahead. Every single step you take forward moves you the exact same distance upward.
We often write a linear function as y = mx + b. The letter 'm' stands for the slope, which tells us how steep our line is, while 'b' is the y-intercept, showing where we start on the vertical axis.
Think of the slope as 'rise over run'. For every step we run to the right, how many units do we rise up? If the slope is positive, we climb up; if it's negative, we slide down!
✏️ Worked example
Graph the linear function: y = 2x + 1
Identify the y-intercept (b), which is 1. This means the line crosses the vertical y-axis at the point (0, 1). Plot this point first.
Identify the slope (m), which is 2. We can think of this as the fraction 2/1.
Use the slope 'rise over run' (2/1) to find your next point. From (0, 1), run 1 unit to the right, and rise 2 units up. This lands you at (1, 3).
Draw a straight line passing directly through both points (0, 1) and (1, 3) to complete your graph!
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