Fix the mistake: Linear Functions ② Equations and Graphs

Equations and Graphs ① Graphs of Linear Equations in Two Variables

The graph of an equation of the form ax + by = c (a linear equation in two variables) is also a straight line. Solving for y gives the form y=ax+b.

Example ①
Draw the graph of 2x + y = 4.
Answer: y=−2x+4. A line with intercept 4 and slope −2. Alternatively, connect the two points x=0→y=4 and y=0→x=2.

Graphs of x=constant and y=constant

The graph of x=a is a vertical line parallel to the y-axis, and the graph of y=b is a horizontal line parallel to the x-axis.

Key Points
  • Transform ax+by=c into y=-(a/b)x+c/b and draw the graph
  • Graph of x=3: a vertical line passing through the point (3,0)
  • Graph of y=−2: a horizontal line passing through the point (0,−2)

Practice Problems

  1. Solve 3x − y = 6 for y, and find the slope and intercept of the graph.
  2. What kind of line is the graph of x = −2?

Answers and Explanations

  1. Answer: y=3x−6. Slope 3, intercept −6.
  2. Answer: A line passing through the point (−2, 0) and parallel to the y-axis (a vertical line).

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