Greetings!
Question Seven:
To find the slope given two points, we can use the slope formula:
[tex]m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}} [/tex]
Input the points: (-11,5) (-6,1)
[tex]m= \frac{1-5}{-6-(-11)} [/tex]
Simplify the equation:
[tex]m= \frac{-4}{5} [/tex]
A parallel slope would be identical to this slope.
Therefore, the answer is B:
[tex]\boxed{m_{2}= \frac{-4}{5}}[/tex]
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Question Eight:
This question essentially asks you to rearrange the equation into slope y-intercept form:
[tex]y=mx+b[/tex]
Rearrange the equation:
[tex]8x+7y=51[/tex]
[tex]7y=-8x-51[/tex]
[tex]y=\frac{-8x-51}{7}[/tex]
[tex]y=\frac{-8}{7}x-\frac{51}{7}[/tex]
The slope (rate of change) is [tex]\frac{-8}{7}[/tex]
Therefore the answer is F:
[tex]\boxed{m=\frac{-8}{7} }[/tex]
I hope this helped!
-Benjamin
