Answer :
To graph the equation [tex]\(8x - 4y = 56\)[/tex] and find the missing values in the coordinate pairs, we'll follow a step-by-step process. Let's start by finding the missing [tex]\(y\)[/tex] values for given [tex]\(x\)[/tex] values, and then determine the missing [tex]\(x\)[/tex] value for a given [tex]\(y\)[/tex] value.
### Step 1: Solving for [tex]\(y\)[/tex] when given [tex]\(x\)[/tex]
#### Point [tex]\((-10, y)\)[/tex]
1. Substitute [tex]\(x = -10\)[/tex] into the equation:
[tex]\[ 8(-10) - 4y = 56 \][/tex]
2. Simplify and solve for [tex]\(y\)[/tex]:
[tex]\[ -80 - 4y = 56 \\ -4y = 56 + 80 \\ -4y = 136 \\ y = \frac{136}{-4} \\ y = -34 \][/tex]
Therefore, the point is [tex]\((-10, -34)\)[/tex].
#### Point [tex]\((0, y)\)[/tex]
1. Substitute [tex]\(x = 0\)[/tex] into the equation:
[tex]\[ 8(0) - 4y = 56 \][/tex]
2. Simplify and solve for [tex]\(y\)[/tex]:
[tex]\[ -4y = 56 \\ y = \frac{56}{-4} \\ y = -14 \][/tex]
Therefore, the point is [tex]\((0, -14)\)[/tex].
#### Point [tex]\((2, y)\)[/tex]
1. Substitute [tex]\(x = 2\)[/tex] into the equation:
[tex]\[ 8(2) - 4y = 56 \][/tex]
2. Simplify and solve for [tex]\(y\)[/tex]:
[tex]\[ 16 - 4y = 56 \\ -4y = 56 - 16 \\ -4y = 40 \\ y = \frac{40}{-4} \\ y = -10 \][/tex]
Therefore, the point is [tex]\((2, -10)\)[/tex].
#### Point [tex]\((4, y)\)[/tex]
1. Substitute [tex]\(x = 4\)[/tex] into the equation:
[tex]\[ 8(4) - 4y = 56 \][/tex]
2. Simplify and solve for [tex]\(y\)[/tex]:
[tex]\[ 32 - 4y = 56 \\ -4y = 56 - 32 \\ -4y = 24 \\ y = \frac{24}{-4} \\ y = -6 \][/tex]
Therefore, the point is [tex]\((4, -6)\)[/tex].
### Step 2: Solving for [tex]\(x\)[/tex] when given [tex]\(y = 0\)[/tex]
#### Point [tex]\((x, 0)\)[/tex]
1. Substitute [tex]\(y = 0\)[/tex] into the equation:
[tex]\[ 8x - 4(0) = 56 \][/tex]
2. Simplify and solve for [tex]\(x\)[/tex]:
[tex]\[ 8x = 56 \\ x = \frac{56}{8} \\ x = 7 \][/tex]
Therefore, the point is [tex]\((7, 0)\)[/tex].
### Summary of Solutions
- The coordinate pair [tex]\((-10, \square)\)[/tex] is [tex]\((-10, -34)\)[/tex].
- The coordinate pair [tex]\((0, \square)\)[/tex] is [tex]\((0, -14)\)[/tex].
- The coordinate pair [tex]\((2, \square)\)[/tex] is [tex]\((2, -10)\)[/tex].
- The coordinate pair [tex]\((4, \square)\)[/tex] is [tex]\((4, -6)\)[/tex].
- The coordinate pair [tex]\((\square, 0)\)[/tex] is [tex]\((7, 0)\)[/tex].
With these points, you can now plot the graph of the equation [tex]\(8x - 4y = 56\)[/tex]. The line should pass through the points [tex]\((-10, -34)\)[/tex], [tex]\((0, -14)\)[/tex], [tex]\((2, -10)\)[/tex], [tex]\((4, -6)\)[/tex], and [tex]\((7, 0)\)[/tex].
### Step 1: Solving for [tex]\(y\)[/tex] when given [tex]\(x\)[/tex]
#### Point [tex]\((-10, y)\)[/tex]
1. Substitute [tex]\(x = -10\)[/tex] into the equation:
[tex]\[ 8(-10) - 4y = 56 \][/tex]
2. Simplify and solve for [tex]\(y\)[/tex]:
[tex]\[ -80 - 4y = 56 \\ -4y = 56 + 80 \\ -4y = 136 \\ y = \frac{136}{-4} \\ y = -34 \][/tex]
Therefore, the point is [tex]\((-10, -34)\)[/tex].
#### Point [tex]\((0, y)\)[/tex]
1. Substitute [tex]\(x = 0\)[/tex] into the equation:
[tex]\[ 8(0) - 4y = 56 \][/tex]
2. Simplify and solve for [tex]\(y\)[/tex]:
[tex]\[ -4y = 56 \\ y = \frac{56}{-4} \\ y = -14 \][/tex]
Therefore, the point is [tex]\((0, -14)\)[/tex].
#### Point [tex]\((2, y)\)[/tex]
1. Substitute [tex]\(x = 2\)[/tex] into the equation:
[tex]\[ 8(2) - 4y = 56 \][/tex]
2. Simplify and solve for [tex]\(y\)[/tex]:
[tex]\[ 16 - 4y = 56 \\ -4y = 56 - 16 \\ -4y = 40 \\ y = \frac{40}{-4} \\ y = -10 \][/tex]
Therefore, the point is [tex]\((2, -10)\)[/tex].
#### Point [tex]\((4, y)\)[/tex]
1. Substitute [tex]\(x = 4\)[/tex] into the equation:
[tex]\[ 8(4) - 4y = 56 \][/tex]
2. Simplify and solve for [tex]\(y\)[/tex]:
[tex]\[ 32 - 4y = 56 \\ -4y = 56 - 32 \\ -4y = 24 \\ y = \frac{24}{-4} \\ y = -6 \][/tex]
Therefore, the point is [tex]\((4, -6)\)[/tex].
### Step 2: Solving for [tex]\(x\)[/tex] when given [tex]\(y = 0\)[/tex]
#### Point [tex]\((x, 0)\)[/tex]
1. Substitute [tex]\(y = 0\)[/tex] into the equation:
[tex]\[ 8x - 4(0) = 56 \][/tex]
2. Simplify and solve for [tex]\(x\)[/tex]:
[tex]\[ 8x = 56 \\ x = \frac{56}{8} \\ x = 7 \][/tex]
Therefore, the point is [tex]\((7, 0)\)[/tex].
### Summary of Solutions
- The coordinate pair [tex]\((-10, \square)\)[/tex] is [tex]\((-10, -34)\)[/tex].
- The coordinate pair [tex]\((0, \square)\)[/tex] is [tex]\((0, -14)\)[/tex].
- The coordinate pair [tex]\((2, \square)\)[/tex] is [tex]\((2, -10)\)[/tex].
- The coordinate pair [tex]\((4, \square)\)[/tex] is [tex]\((4, -6)\)[/tex].
- The coordinate pair [tex]\((\square, 0)\)[/tex] is [tex]\((7, 0)\)[/tex].
With these points, you can now plot the graph of the equation [tex]\(8x - 4y = 56\)[/tex]. The line should pass through the points [tex]\((-10, -34)\)[/tex], [tex]\((0, -14)\)[/tex], [tex]\((2, -10)\)[/tex], [tex]\((4, -6)\)[/tex], and [tex]\((7, 0)\)[/tex].
