Question

module 1: question 16
line m is defined by ( 17y - 5x = 13 ). line n is perpendicular to line m in the xy - plane. what is the slope of line n?

module 2a: question 9
pete made 40 liters of lemonade. pete then filled c small cups and b large bottles with all of the lemonade he made. the equation ( 0.8c + 1.2b = 40 ) represents this situation. which is the best interpretation of ( 0.8c ) in this context?
a) the number of liters of lemonade in each small cup.
b) the number of liters of lemonade in each large bottle.
c) the total number of liters of lemonade in the c small cups.
d) the total number of liters of lemonade in the b large bottles.

module 2a: question 15
the table gives the coordinates for two points on a line in the xy - plane. the x - intercept of the line is ( (b, a - 4) ), where a and b are constants. what is the value of b?

x	y
52	( a + 4 )

Explanation:

Module 1: Question 16

Step1: Convert to slope-intercept form

Rearrange line $m$ to $y=mx+b$:
$$17y - 5x = 13 \implies 17y = 5x + 13 \implies y = \frac{5}{17}x + \frac{13}{17}$$

Step2: Find perpendicular slope

Perpendicular slope is negative reciprocal:
$$m_{\perp} = -\frac{17}{5}$$

In the equation $0.8c + 1.2b = 40$, $c$ is the number of small cups. Multiplying the number of small cups by $0.8$ (the volume per small cup) gives the total volume of lemonade in all small cups.

Step1: Calculate slope of the line

Use the two given points:
$$m = \frac{(a+4) - a}{52 - 53} = \frac{4}{-1} = -4$$

Step2: Set up equation for x-intercept

The x-intercept $(b, a-4)$ lies on the line. Use point $(53, a)$ and slope:
$$\frac{(a-4) - a}{b - 53} = -4$$

Step3: Solve for $b$

Simplify and solve the equation:
$$\frac{-4}{b - 53} = -4 \implies -4 = -4(b - 53) \implies 1 = b - 53 \implies b = 54$$

Answer:

$-\frac{17}{5}$

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Module 2A: Question 9