Graphing Equations in Intercept Form

Hello Math Students! Today, we explored how to graph equations presented in the standard form, often referred to as intercept form: $Ax + By = C$. This method relies on finding the x and y intercepts of the line.

Key Concepts:

  • Standard Form: Recognizing that an equation is in the form $Ax + By = C$ is the first step. This is also known as Intercept form.
  • X-intercept: The point where the line crosses the x-axis. To find it, substitute $y = 0$ into the equation and solve for $x$.
  • Y-intercept: The point where the line crosses the y-axis. To find it, substitute $x = 0$ into the equation and solve for $y$.
  • Slope-Intercept Form: Another useful form is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. You can convert from standard form to slope-intercept form by isolating $y$.

Steps to Graphing:

  1. Find the x-intercept: Let $y = 0$ and solve for $x$. This gives you the point $(x, 0)$.
  2. Find the y-intercept: Let $x = 0$ and solve for $y$. This gives you the point $(0, y)$.
  3. Plot the intercepts: Plot the points you found on the coordinate plane.
  4. Draw the line: Draw a straight line through the two points. Extend the line to fill the graph.

Example:

Let's graph the equation $2x + 3y = 12$

  1. Find the x-intercept: Let $y = 0$.
    $2x + 3(0) = 12$
    $2x = 12$
    $x = 6$
    The x-intercept is $(6, 0)$.
  2. Find the y-intercept: Let $x = 0$.
    $2(0) + 3y = 12$
    $3y = 12$
    $y = 4$
    The y-intercept is $(0, 4)$.
  3. Plot and Draw: Plot the points $(6, 0)$ and $(0, 4)$ and draw the line that passes through them.

Remember!

  • The slope, often denoted as $m$, represents the rate of change of the line. It is calculated as rise over run. For instance, if $m = -2/3$, it means that for every 3 units you move to the right (run), you move 2 units down (rise). The y-intercept is always a point of the form (0, b).

Bonus Point!

Don't forget! Write the word paperclip on your warm-up to get a bonus point on your next test.

Homework:

Complete problems Pg. 87 # 38-48 even to practice graphing equations in intercept form. Keep up the great work!

Class Notes: