Graphing Linear Functions
Graphing linear functions by plotting points is a foundational skill in Grade 11 enVision Algebra 1 (Chapter 3: Linear Functions). Because linear functions always form straight lines, only two coordinate pairs are needed to draw the complete graph, though plotting a third point verifies accuracy. Students create a table of x-values, compute the corresponding f(x) values from the equation, then connect the plotted points with a line. This process connects algebraic function evaluation to visual representation.
Key Concepts
We can construct a graph for a linear function by plotting points whose coordinates satisfy the equation. Since linear functions form straight lines, we only need two points to draw the complete graph, though plotting a third point helps verify accuracy.
Common Questions
How many points do you need to graph a linear function?
You need at least two points, since two points uniquely determine a straight line. Plotting a third point is recommended to verify there are no calculation errors.
What is the general process for graphing a linear function?
Create a table with at least two x-values, evaluate the function to find corresponding f(x) values, plot the coordinate pairs (x, f(x)), then draw a line through them.
Why do linear functions always form straight lines?
A linear function has the form f(x) = mx + b, where x appears only to the first power. The constant rate of change (slope m) produces a straight line.
Which x-values should you choose when making a table for graphing?
Choose values that are easy to compute, typically including 0 (which gives the y-intercept) and simple positive and negative integers.
What is the y-intercept in a linear function f(x) = mx + b?
The y-intercept is b — the point (0, b) where the line crosses the y-axis, found by substituting x = 0 into the equation.
How do you verify that your graph is correct?
Plot a third point by computing f(x) for another x-value. If it lies on the line you drew, the graph is correct.