To find the intercepts of the equation [tex]\(16x - 4y = -32\)[/tex], we follow these steps:
### Finding the x-intercept:
The x-intercept is the value of [tex]\(x\)[/tex] where the graph of the equation crosses the x-axis. This occurs when [tex]\(y = 0\)[/tex].
1. Substitute [tex]\(y = 0\)[/tex] into the equation:
[tex]\[16x - 4(0) = -32\][/tex]
[tex]\[16x = -32\][/tex]
2. Solve for [tex]\(x\)[/tex]:
[tex]\[x = \frac{-32}{16}\][/tex]
[tex]\[x = -2\][/tex]
So, the x-intercept is [tex]\((-2, 0)\)[/tex].
### Finding the y-intercept:
The y-intercept is the value of [tex]\(y\)[/tex] where the graph of the equation crosses the y-axis. This occurs when [tex]\(x = 0\)[/tex].
1. Substitute [tex]\(x = 0\)[/tex] into the equation:
[tex]\[16(0) - 4y = -32\][/tex]
[tex]\[-4y = -32\][/tex]
2. Solve for [tex]\(y\)[/tex]:
[tex]\[y = \frac{-32}{-4}\][/tex]
[tex]\[y = 8\][/tex]
So, the y-intercept is [tex]\((0, 8)\)[/tex].
### Summary:
- The x-intercept of the equation [tex]\(16x - 4y = -32\)[/tex] is [tex]\((-2, 0)\)[/tex].
- The y-intercept of the equation [tex]\(16x - 4y = -32\)[/tex] is [tex]\((0, 8)\)[/tex].
