In coordinate geometry, the x-intercept and y-intercept of a line are the points at which the line crosses the x-axis and y-axis, respectively. These points are important because they give a quick visual representation of where the line is located in the coordinate plane. In this blog post, we will go over the steps to find the x-intercept and y-intercept of a line.

Step 1: Write the equation of the line in slope-intercept form (y = mx + b). The slope-intercept form is the most common form in which the equation of a line is written. This form makes it easy to identify the slope (m) and y-intercept (b) of the line.

Step 2: Find the x-intercept by setting y equal to zero. To find the x-intercept, we need to find the point at which the line crosses the x-axis. The x-axis is the line where y = 0, so we can set y equal to zero in our equation. This will give us an equation in terms of x, which we can then solve for.

Step 3: Find the y-intercept by setting x equal to zero. To find the y-intercept, we need to find the point at which the line crosses the y-axis. The y-axis is the line where x = 0, so we can set x equal to zero in our equation. This will give us an equation in terms of y, which we can then solve for.

Step 4: Substitute the values of x and y back into the original equation to check your work.

An example: Find the x and y intercepts of the line y = 2x + 3

Step 1: Write the equation in slope-intercept form. y = 2x + 3

Step 2: Find the x-intercept by setting y equal to zero. 0 = 2x + 3

Step 3: Solve for x. -3 = 2x x = -3/2

Step 4: Find the y-intercept by setting x equal to zero. y = 2(0) + 3 y = 3

Step 5: check your work. y = 2(-3/2) + 3 y = 0

So the x-intercept is (-3/2,0) and the y-intercept is (0,3)

In conclusion, finding the x-intercept and y-intercept of a line is a relatively simple process that can be done by setting x or y equal to zero in the equation of the line, solving for the other variable, and then checking your work. Understanding the x-intercept and y-intercept of a line can help you better understand the location and slope of the line in the coordinate plane.