Question

vicky is studying french. she spends 1 hour reviewing each old chapter. she also spends 1.5 hours learning each new chapter. she spends at least 10 hours per weeks studying french. which graph could represent the possible number of old chapters vicky reviews, x, and new chapters vicky learns, y, each week? answer attempt 1 out of 2 a b c d

Explanation:

Step1: Formulate the inequality

Vicky spends 1 hour on each old chapter (\(x\)) and 1.5 hours on each new chapter (\(y\)), with total time at least 10 hours. So the inequality is \(x + 1.5y \geq 10\). Rewrite it in slope - intercept form (\(y=mx + b\)):

$$
LATEXBLOCK0
$$

The boundary line has a slope of \(-\frac{2}{3}\) (negative, decreasing) and a y - intercept of \(\frac{20}{3}\approx6.67\). Since the inequality is \(y\geq\), we shade above the line. Also, \(x\geq0\) and \(y\geq0\) because the number of chapters can't be negative.

Step2: Analyze the line type and shading

• The boundary line should be dashed or solid? Since the inequality is "at least" (≥), the boundary line is solid (because the points on the line are included in the solution set).
• Shading direction: We shade the region where \(y\geq-\frac{2}{3}x+\frac{20}{3}\), which is above the line. Also, \(x\) (old chapters) and \(y\) (new chapters) are non - negative, so we are in the first quadrant.
• Looking at the options:
• Option A: Shading below the line, incorrect.
• Option B: Shading above the solid line (since the line is solid and shading is above), and in the first quadrant, this matches our inequality \(y\geq-\frac{2}{3}x+\frac{20}{3},x\geq0,y\geq0\).
• Option C: Dashed line, but our boundary line should be solid (because of ≥), incorrect.
• Option D: Dashed line, incorrect.

Answer:

B