To find the x and y intercepts of the equation x + 4y = 8, we can follow these steps:
Finding the X-Intercept
The x-intercept occurs when y = 0. To find it, we substitute y with 0 in the equation:
x + 4(0) = 8
This simplifies to:
x = 8
So, the x-intercept is at the point (8, 0).
Finding the Y-Intercept
The y-intercept occurs when x = 0. To find it, we substitute x with 0 in the equation:
0 + 4y = 8
This simplifies to:
4y = 8
By dividing both sides by 4, we find:
y = 2
So, the y-intercept is at the point (0, 2).
Plotting the Intercepts
Now that we have the intercepts, we can plot them on a graph:
- X-intercept: (8, 0)
- Y-intercept: (0, 2)
To graph the equation, place these points on the coordinate plane and draw a straight line through them. The line will represent the equation x + 4y = 8.
This method of finding intercepts gives us key points to visualize the relationship represented by the equation.