To graph the equation [tex]\(8x - 4y = 56\)[/tex] and find the missing values in the given coordinate pairs, we first rearrange the equation to solve for [tex]\(y\)[/tex]:
Starting with the equation:
[tex]\[ 8x - 4y = 56 \][/tex]
We isolate [tex]\(y\)[/tex]:
[tex]\[ -4y = 56 - 8x \][/tex]
[tex]\[ y = \frac{8x - 56}{4} \][/tex]
Simplifying the right side:
[tex]\[ y = 2x - 14 \][/tex]
Now that we have the equation in the form [tex]\(y = 2x - 14\)[/tex], we can use it to find the missing coordinate values for each pair:
1. For [tex]\((-10, \square)\)[/tex]:
Plug [tex]\(x = -10\)[/tex] into [tex]\(y = 2x - 14\)[/tex]:
[tex]\[ y = 2(-10) - 14 \][/tex]
[tex]\[ y = -20 - 14 \][/tex]
[tex]\[ y = -34 \][/tex]
So, the coordinate pair is [tex]\((-10, -34)\)[/tex].
2. For [tex]\((0, \square)\)[/tex]:
Plug [tex]\(x = 0\)[/tex] into [tex]\(y = 2x - 14\)[/tex]:
[tex]\[ y = 2(0) - 14 \][/tex]
[tex]\[ y = -14 \][/tex]
So, the coordinate pair is [tex]\((0, -14)\)[/tex].
3. For [tex]\((2, \square)\)[/tex]:
Plug [tex]\(x = 2\)[/tex] into [tex]\(y = 2x - 14\)[/tex]:
[tex]\[ y = 2(2) - 14 \][/tex]
[tex]\[ y = 4 - 14 \][/tex]
[tex]\[ y = -10 \][/tex]
So, the coordinate pair is [tex]\((2, -10)\)[/tex].
4. For [tex]\((4, \square)\)[/tex]:
Plug [tex]\(x = 4\)[/tex] into [tex]\(y = 2x - 14\)[/tex]:
[tex]\[ y = 2(4) - 14 \][/tex]
[tex]\[ y = 8 - 14 \][/tex]
[tex]\[ y = -6 \][/tex]
So, the coordinate pair is [tex]\((4, -6)\)[/tex].
5. For [tex]\((\square, 0)\)[/tex]:
Set [tex]\(y = 0\)[/tex] and solve for [tex]\(x\)[/tex] in the equation [tex]\(y = 2x - 14\)[/tex]:
[tex]\[ 0 = 2x - 14 \][/tex]
[tex]\[ 2x = 14 \][/tex]
[tex]\[ x = 7 \][/tex]
So, the coordinate pair is [tex]\((7, 0)\)[/tex].
The resulting completed pairs are:
- [tex]\((-10, -34)\)[/tex]
- [tex]\((0, -14)\)[/tex]
- [tex]\((2, -10)\)[/tex]
- [tex]\((4, -6)\)[/tex]
- [tex]\((7, 0)\)[/tex]
