Question

ation.

1. ( y = -\frac{1}{5}x - 5 )

x	y
-4
0
6
-8
7

1. ( y = x - 9 )

x	y
0	-9
7	-2
-3	-12
3	-6
-9	-18

1. ( y = -9x )

x	y
-6	54
-8	72

Explanation:

Step1: For \( x = -4 \) in \( y = -\frac{1}{5}x - 5 \)

Substitute \( x=-4 \) into the equation: \( y = -\frac{1}{5}(-4) - 5=\frac{4}{5}-5=\frac{4 - 25}{5}=-\frac{21}{5}=-4.2 \)

Step2: For \( x = 0 \) in \( y = -\frac{1}{5}x - 5 \)

Substitute \( x = 0 \): \( y=-\frac{1}{5}(0)-5=-5 \)

Step3: For \( x = 6 \) in \( y = -\frac{1}{5}x - 5 \)

Substitute \( x = 6 \): \( y=-\frac{1}{5}(6)-5=-\frac{6}{5}-5=\frac{-6 - 25}{5}=-\frac{31}{5}=-6.2 \)

Step4: For \( x = -8 \) in \( y = -\frac{1}{5}x - 5 \)

Substitute \( x=-8 \): \( y = -\frac{1}{5}(-8)-5=\frac{8}{5}-5=\frac{8 - 25}{5}=-\frac{17}{5}=-3.4 \)

Step5: For \( x = 7 \) in \( y = -\frac{1}{5}x - 5 \)

Substitute \( x = 7 \): \( y=-\frac{1}{5}(7)-5=-\frac{7}{5}-5=\frac{-7 - 25}{5}=-\frac{32}{5}=-6.4 \)

For problem 10, we can verify the given \( y \) values:

• When \( x = 0 \), \( y=0 - 9=-9 \) (matches)
• When \( x = 7 \), \( y=7 - 9=-2 \) (matches)
• When \( x=-3 \), \( y=-3 - 9=-12 \) (matches)
• When \( x = 3 \), \( y=3 - 9=-6 \) (matches)
• When \( x=-9 \), \( y=-9 - 9=-18 \) (matches)

For problem 11, for \( y=-9x \):

• When \( x=-6 \), \( y=-9(-6)=54 \) (matches)
• When \( x=-8 \), \( y=-9(-8)=72 \) (matches)

Answer:

For problem 9, the \( y \) values are \(-\frac{21}{5}\) (or \(-4.2\)), \(-5\), \(-\frac{31}{5}\) (or \(-6.2\)), \(-\frac{17}{5}\) (or \(-3.4\)), \(-\frac{32}{5}\) (or \(-6.4\)) for \( x=-4,0,6,-8,7 \) respectively. For problem 10, the given \( y \) values are correct. For problem 11, the given \( y \) values are correct.