How do you find the x and y intercepts of a graph from its equation?

Questions : How do you find the x and y intercepts of a graph from its equation?

Answer:  

 To find the x-intercept(s), set $y = 0$ in the equation and solve for $x$. To find the y-intercept(s), set $x = 0$ and solve for $y$.

Additional Information

Absolutely! Here's how to find the x and y intercepts of a graph from its equation:

Understanding Intercepts

• x-intercept: The point where the graph crosses the x-axis. At this point, the y-coordinate is always zero.
• y-intercept: The point where the graph crosses the y-axis.¹ At this point, the x-coordinate is always zero.

Steps to Find Intercepts

1. To find the x-intercept(s):

   • Substitute y = 0 into the equation.²
   • Solve the equation for x.
   • The x-value(s) you find are the x-intercept(s). Write them as (x, 0) coordinates.

2. To find the y-intercept(s):

   • Substitute x = 0 into the equation.³
   • Solve the equation for y.
   • The y-value(s) you find are the y-intercept(s). Write them as (0, y) coordinates.

Example

Let's find the intercepts of the equation: 3x + 2y = 6

• x-intercept:

  • Substitute y = 0: 3x + 2(0) = 6
  • Solve for x: 3x = 6 => x = 2
  • x-intercept: (2, 0)

• y-intercept:

  • Substitute x = 0: 3(0) + 2y = 6
  • Solve for y: 2y = 6 => y = 3
  • y-intercept: (0, 3)

Important Notes

• Linear Equations: Linear equations (equations that graph as straight lines) will have at most one x-intercept and one y-intercept.
• Non-linear Equations: More complex equations can have multiple x-intercepts and/or multiple y-intercepts.
• Not all graphs have intercepts: For example, a horizontal line that lies above or below the x-axis will not have an x-intercept.

Let me know if you'd like to try another example!

CBSE / NCERT / SAT/ UPSC 

You Can Translate It In Your Language :-

  EDUTICAL

Mock Test Click Here

Maddhamik Previous Year Solution Click Here

CBSE CLASS 10 History Notes Click Here

If you like this content, please CLICK any of the Ads In This Page.

Thank you 

Team EDUTICAL