Medium📚 Linear Functions

Graph a Linear Function

Grades 8-9Key Stage 3-4Årskurs 8-9

Problem

Graph the linear function: f(x) = 2x - 3

📝Step-by-Step Solution

Identify slope and y-intercept

The function f(x) = 2x - 3 is in slope-intercept form (y = mx + b). Slope m = 2, y-intercept b = -3.

m = 2, b = -3

Plot the y-intercept

The y-intercept is where the line crosses the y-axis. Plot the point (0, -3).

Point 1: (0, -3)

Use slope to find another point

Slope = 2 = 2/1 means "rise 2, run 1". From (0, -3), go up 2 and right 1 to get (1, -1).

Point 2: (1, -1)

Find a third point (optional)

From (1, -1), go up 2 and right 1 again to get (2, 1). Or use the equation: f(2) = 2(2) - 3 = 1.

Point 3: (2, 1)

Draw the line

Connect the points with a straight line. Extend the line with arrows on both ends to show it continues infinitely.

✅Final Answer

Line passing through (0, -3), (1, -1), (2, 1) with slope 2

To graph any linear function: (1) Find the y-intercept (b) and plot it, (2) Use the slope (m) as rise/run to find more points, (3) Connect with a straight line. If slope is negative, go down instead of up for the rise.

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