Question

3a. (2 pts.) given the table, choose the equation that best matches the data.

x	0	1	2	3	4
y	-9	-7	-5	-3	-1

• y - 2x = 9
• 1/2 x + y = 2
• 2x - y = 9
• -9x - y = 9

3b. (2 pts.) given the table, choose the equation that best matches the data.

x	y
1	8
2	12
3	16
4	20

• 2x - y = -4
• -4x + y = 4
• 1x + 4y = 6
• -1/4x + y = 4

Explanation:

3a

Step1: Test \(x = 0, y=-9\) in each equation

• For \(y - 2x=9\): \(-9-2(0)=-9

eq9\)

• For \(2x - y = 9\): \(2(0)-(-9)=9\), works for \((0, -9)\)
• For \(\frac{1}{2}x + y=2\): \(\frac{1}{2}(0)+(-9)=-9

eq2\)

• For \(-9x - y = 9\): \(-9(0)-(-9)=9\), works for \((0, -9)\)

Step2: Test \(x = 1, y=-7\) in remaining equations

• For \(2x - y = 9\): \(2(1)-(-7)=9\), works.
• For \(-9x - y = 9\): \(-9(1)-(-7)=-2

eq9\)

Step1: Test \(x = 1, y = 8\) in each equation

• For \(2x - y=-4\): \(2(1)-8=-6

eq-4\)

• For \(-4x + y = 4\): \(-4(1)+8 = 4\), works for \((1, 8)\)
• For \(1x + 4y = 6\): \(1 + 32 = 33

eq6\)

• For \(-\frac{1}{4}x + y = 4\): \(-\frac{1}{4}(1)+8=\frac{31}{4}

eq4\)

Step2: Verify with \(x = 2, y = 12\) in \(-4x + y = 4\)

\(-4(2)+12 = 4\), works.

Answer:

\(2x - y = 9\)

3b