To graph the linear equation [tex]\(4y + 16x = 32\)[/tex] by plotting points, we first need to solve for [tex]\(y\)[/tex] in terms of [tex]\(x\)[/tex]. Here is the step-by-step process to find [tex]\(y\)[/tex] for each given value of [tex]\(x\)[/tex]:
1. Solve for [tex]\(y\)[/tex]:
Given the equation:
[tex]\[
4y + 16x = 32
\][/tex]
Isolate [tex]\(y\)[/tex] by following these steps:
[tex]\[
4y = 32 - 16x
\][/tex]
[tex]\[
y = \frac{32 - 16x}{4}
\][/tex]
Simplifying the equation:
[tex]\[
y = 8 - 4x
\][/tex]
2. Fill in the table for each given value of [tex]\(x\)[/tex]:
[tex]\(\mathbf{x = -2}\)[/tex]
[tex]\[
y = 8 - 4(-2) = 8 + 8 = 16
\][/tex]
Ordered pair: [tex]\((-2, 16)\)[/tex]
[tex]\(\mathbf{x = -1}\)[/tex]
[tex]\[
y = 8 - 4(-1) = 8 + 4 = 12
\][/tex]
Ordered pair: [tex]\((-1, 12)\)[/tex]
[tex]\(\mathbf{x = 0}\)[/tex]
[tex]\[
y = 8 - 4(0) = 8
\][/tex]
Ordered pair: [tex]\((0, 8)\)[/tex]
[tex]\(\mathbf{x = 1}\)[/tex]
[tex]\[
y = 8 - 4(1) = 8 - 4 = 4
\][/tex]
Ordered pair: [tex]\((1, 4)\)[/tex]
[tex]\(\mathbf{x = 2}\)[/tex]
[tex]\[
y = 8 - 4(2) = 8 - 8 = 0
\][/tex]
Ordered pair: [tex]\((2, 0)\)[/tex]
3. Summary of the table and ordered pairs:
```
x y Ordered Pair
-2 16 (-2, 16)
-1 12 (-1, 12)
0 8 (0, 8)
1 4 (1, 4)
2 0 (2, 0)
```
4. Graphing the equation:
- Plot the ordered pairs [tex]\((-2, 16)\)[/tex], [tex]\((-1, 12)\)[/tex], [tex]\((0, 8)\)[/tex], [tex]\((1, 4)\)[/tex], and [tex]\((2, 0)\)[/tex] on a coordinate plane.
- Draw a straight line through these points, as they all lie on the line representing the equation [tex]\(4y + 16x = 32\)[/tex].
By following these steps, we can successfully graph the linear equation by plotting the points calculated for different values of [tex]\(x\)[/tex].
