Question

7y ≤ 5x - 35
answer
key
the line will be drawn once all required data is provided and will update whenever a value is updated. the regions will be added once the line is drawn.
choose the type of boundary line:
solid (—) dashed (—)
enter two points on the boundary line:
( , ) ( , )
select the region you wish to be shaded:
a b

Explanation:

Step1: Simplify the inequality

First, we simplify the inequality \(7y \leq 5x - 35\) by dividing both sides by 7:
\(y \leq \frac{5}{7}x - 5\)
Since the inequality is \(\leq\), the boundary line will be solid (because the inequality includes equality, so the line is part of the solution set).

Step2: Find two points on the boundary line

The boundary line is \(y=\frac{5}{7}x - 5\). We can find two points by choosing values for \(x\) and solving for \(y\).

• Let \(x = 0\):

\(y=\frac{5}{7}(0)-5=- 5\), so one point is \((0, - 5)\).

• Let \(x = 7\):

\(y=\frac{5}{7}(7)-5=5 - 5=0\), so another point is \((7,0)\).

Step3: Determine the shaded region

To determine the shaded region, we can test a point not on the line. Let's test the origin \((0,0)\):
Substitute \(x = 0\) and \(y = 0\) into the original inequality \(7y\leq5x - 35\):
\(7(0)\leq5(0)-35\)
\(0\leq - 35\), which is false. So the origin is not in the solution set. The solution set (the region to be shaded) is the region below the line \(y=\frac{5}{7}x - 5\) (since the inequality is \(y\leq\frac{5}{7}x - 5\)).

Answer:

• Type of boundary line: Solid (\(-\))
• Two points on the boundary line: \((0, - 5)\), \((7,0)\)
• Shaded region: The region below the line (the region that does not include the origin, so if the options are A and B, we need to see which one is below the line. Since when we tested \((0,0)\) it was not in the solution, the shaded region is the one that satisfies \(y\leq\frac{5}{7}x - 5\), which is the region below the line \(y = \frac{5}{7}x-5\))