Section 2.4: Graphing Practice

In this section, we will practice graphing linear equations using different forms.

Use slope-intercept form, point-slope form, or standard form as needed. Remember:

  • Two points are sufficient to draw a line.
  • Label the axes and points clearly.
  • Check your slope and intercepts before plotting.

Example 1

Graph the line \( y = -x + 4 \).

Step 1: Find two points. \( x=0 \): \( y=4 \) → (0,4) \( x=2 \): \( y=-2+4=2 \) → (2,2)

Step 2: Plot the points and draw a straight line through them.

Example 2

Graph the line passing through (1,3) with slope \( \frac{1}{2} \).

Step 1: Use point-slope form: \( y - 3 = \frac{1}{2}(x - 1) \) Step 2: Pick another point, e.g., \( x=3 \) → \( y-3 = \frac{1}{2}(2) \) → \( y = 4 \) → (3,4)

Step 3: Plot the points (1,3) and (3,4) and draw the line.

Practice Problems

  1. Graph \( y = 2x - 1 \).
  2. Graph \( y = -\frac{1}{3}x + 5 \).
  3. Graph the line through points (0,0) and (4,6).
  4. Graph the line passing through (-2,3) with slope -1.
  5. Graph \( 3x + 2y = 6 \) using intercepts.