How can I find the x-intercept and y-intercept of a line on a graph?

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To determine the x-intercept and y-intercept of a line on a graph, you need to follow a few simple steps:

Finding the X-Intercept

The x-intercept is the point where the line crosses the x-axis. This occurs when the value of y is zero. Here’s how to find it:

  1. Identify the equation of the line if it’s given. If not, you may need to extract it from the graph.
  2. Set y equal to zero in the equation of the line.
  3. Solve the equation for x. The solution will give you the x-coordinate of the x-intercept.
  4. Write the x-intercept as an ordered pair (x, 0).

Finding the Y-Intercept

The y-intercept is the point where the line crosses the y-axis. This occurs when the value of x is zero. To find the y-intercept, follow these steps:

  1. Again, start with the equation of the line.
  2. Set x equal to zero.
  3. Solve the equation for y. The result will provide you with the y-coordinate of the y-intercept.
  4. Write the y-intercept as an ordered pair (0, y).

Example

Let’s say you have the equation of a line given by:

y = 2x + 3

To find the x-intercept:

  • Set y to 0: 0 = 2x + 3
  • Solve for x: 2x = -3, so x = -1.5
  • The x-intercept is (-1.5, 0).

To find the y-intercept:

  • Set x to 0: y = 2(0) + 3
  • Solve for y: y = 3
  • The y-intercept is (0, 3).

In conclusion, by following these straightforward steps, you can effortlessly determine the x-intercept and y-intercept from the graph of a line.

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