ANSWER
{},{1},{3},{5},{7},{1,3},{1,5},{1,7},{3,5},{3,7},{5,7},{1,3,5},{1,3,7},{3,5,7},{1,5,7},{1,3,5,7}
EXPLANATION
The given set is {1,3,5,7}.
This set has
subsets.
Where n=4 is the number of elements in the set.
Recall that the null set is a subset of every set and every set is a subset of itself.
The subsets are:
{}
{1},{3},{5},{7}
{1,3},{1,5},{1,7},{3,5},{3,7},{5,7}
{1,3,5},{1,3,7},{3,5,7},{1,5,7}
{1,3,5,7}
So perpendicular lines have <u>slopes that are negative reciprocals</u> to each other, but firstly we need to find the slope of the original equation. The easiest method to find it is to convert this standard form into slope-intercept.
Firstly, subtract 3x on both sides of the equation:
Next, divide both sides by -4 and your slope-intercept form of the original equation is
Now looking at this equation, we see that the slope is 3/4. Now since our new line is perpendicular, this means that <em>its slope is -4/3.</em>
Now that we have the slope, plug that into the m variable and plug in (-4,-5) into the x and y coordinates to solve for the b variable as such:
<u>In short, your new equation is y = -4/3x - 10 1/3.</u>