To determine the intercepts of the linear equation [tex]\(4x + 8y = 64\)[/tex], follow these steps:
### Finding the [tex]\(x\)[/tex]-intercept:
The [tex]\(x\)[/tex]-intercept occurs where the line crosses the [tex]\(x\)[/tex]-axis. At this point, the value of [tex]\(y\)[/tex] is 0. Let’s set [tex]\(y = 0\)[/tex] in the equation and solve for [tex]\(x\)[/tex]:
[tex]\[4x + 8(0) = 64\][/tex]
This simplifies to:
[tex]\[4x = 64\][/tex]
Next, solve for [tex]\(x\)[/tex] by dividing both sides of the equation by 4:
[tex]\[x = \frac{64}{4}\][/tex]
[tex]\[x = 16\][/tex]
So, the [tex]\(x\)[/tex]-intercept is at the point [tex]\( (16, 0) \)[/tex].
### Finding the [tex]\(y\)[/tex]-intercept:
The [tex]\(y\)[/tex]-intercept occurs where the line crosses the [tex]\(y\)[/tex]-axis. At this point, the value of [tex]\(x\)[/tex] is 0. Let’s set [tex]\(x = 0\)[/tex] in the equation and solve for [tex]\(y\)[/tex]:
[tex]\[4(0) + 8y = 64\][/tex]
This simplifies to:
[tex]\[8y = 64\][/tex]
Next, solve for [tex]\(y\)[/tex] by dividing both sides of the equation by 8:
[tex]\[y = \frac{64}{8}\][/tex]
[tex]\[y = 8\][/tex]
So, the [tex]\(y\)[/tex]-intercept is at the point [tex]\((0, 8)\)[/tex].
### Summary:
- [tex]\(x\)[/tex]-intercept: [tex]\( (16, 0) \)[/tex]
- [tex]\(y\)[/tex]-intercept: [tex]\( (0, 8) \)[/tex]
Thus, the intercepts for the given linear equation [tex]\(4x + 8y = 64\)[/tex] are:
[tex]\[x \text {-intercept }(16, 0) \][/tex]
[tex]\[y \text {-intercept }(0, 8) \][/tex]
