Here are the answers to the multiple-choice questions you provided:
Question 1:
The line passes through (0, -7) and (3, -5). The slope (m) can be calculated as:
\[ m = \frac{-5 - (-7)}{3 - 0} = \frac{2}{3} \]
The equation of the line is in the form:
\[ y = \frac{2}{3} x - 7 \]
Since the shading is above the line and there is a solid line, the correct inequality is: Answer: y ≥ (2/3)x - 7
Question 2:
The equation of the line can be determined from the points (1, 4) and (2, 9). The slope (m) is:
\[ m = \frac{9 - 4}{2 - 1} = 5 \]
The equation of the line can be written as:
\[ y - 4 = 5(x - 1) \]
or
\[ y = 5x - 1 \]
Since the shading is below the line, we consider the inequality:
Answer: 5x + y ≤ 1
Question 3:
For the inequality \( y < \frac{3}{4}x - 3 \):
Substituting \( x = 6 \):
\[ y < \frac{3}{4} \cdot 6 - 3 = \frac{18}{4} - 3 = 4.5 - 3 = 1.5 \]
Since 4 is greater than 1.5, the point (6, 4) is above the line.
Answer: No, because (6, 4) is above the line
Question 4:
A dashed horizontal line through (0, 4) indicates that y cannot be equal to 4, and since the shading is below the line:
Answer: y < 4
Question 5:
The maximum y-intercept occurs when \( x = 0 \):
\[ 7(0) + 5y ≤ 200 \rightarrow y ≤ 40 \]
The maximum x-intercept occurs when \( y = 0 \):
\[ 7x + 5(0) ≤ 200 \rightarrow x ≤ \frac{200}{7} \approx 28.57 \]
The inequality indicates that the area below the line is shaded.
Answer: X, Y graph. X range is negative 60 to 44... Below line is shaded.
Question 6:
For the inequality \( 2.5x + 4y ≤ 60 \):
- For 10 bags of chips and 2 jars of salsa: \[ 2.5(10) + 4(2) = 25 + 8 = 33 ≤ 60\]
- For 20 bags of chips and 2 jars of salsa: \[ 2.5(20) + 4(2) = 50 + 8 = 58 ≤ 60\]
- For 14 bags of chips and 5 jars of salsa: \[ 2.5(14) + 4(5) = 35 + 20 = 55 ≤ 60\]
- For 18 bags of chips and 6 jars of salsa: \[ 2.5(18) + 4(6) = 45 + 24 = 69 > 60\] Thus, this is not a solution. Answer: 18 bags of chips and 6 jars of salsa
Question 7:
The inequality \(-4y - x ≥ 7\) can be rewritten as:
\[ -4y \geq x + 7 \]
or
\[ y \leq -\frac{1}{4}x - \frac{7}{4} \]
This indicates shading below the line (solid line).
Answer: Below the solid line
Question 8:
A dashed vertical line through \((-3, 0)\) with shading to the left indicates:
Answer: x < −3
Question 9:
The inequality \( y ≤ \frac{2}{7}x + 1 \) intersects the y-axis at 1 and has a positive slope, meaning it will be true in quadrants I and III (below and including the line).
Answer: I and IV
Question 10:
The line has a positive slope and the shading is above the line. The equation can be manipulated to determine the matching inequality:
Answer: 3x − 2y ≤ 7
Let me know if you have any more questions!