As you may realize, the equation y=-7/4x-2 is already formatted in slope-intercept form, which means that its slope is represented by the "x" coefficient, that is, -7/4.
Lines that are parallel share identical slopes, therefore a line parallel to this would also maintain a slope of -7/4, which would go through the point (4,2),
To solve this problem, you'll want to substitute the first equation into the second or the other way around. The equations given are: 1. 3 paperback books + 5 hardcover books = $80.10; 2. 7 paperback books + 4 hardcover books = $100.65. It is helpful to rearrange the first equation to find 5 hardcover books = $80.10 - 3 paperback books, leading to hardcover book = $16.02 - 0.6 paperback books. Now, substitute this into the second equation: 7 paperback books + 4 ($16.02 - 0.6 paperback books) = $100.65, which simplifies to 7 paperback books + $64.08 - 2.4 paperback books = $100.65. This results in 4.6 paperback books = $100.65 - $64.08 = $36.57, thus paperback book = $7.95. You can then use this price in the first equation to determine the hardcover book price: 3 paperback books + 5 hardcover books = $80.10, substituting gives 3($7.95) + 5 hardcover books = $80.10, which leads to 5 hardcover books = $80.10 - $23.85 = $56.25, therefore hardcover book = $11.25. Hence, the total cost for one paperback and one hardcover book is $7.95 + $11.25 = $19.20.
Question 1: (2.2, -1.4). Question 2: (1.33, 1). Providing a detailed analysis, the equations for the given lines are specified as (1) passing through points (0, 2.5) and (2.2, 1.4), and (2) through (0, -3) and (2.2, -1.4). We are tasked with locating a common solution or intersection of these equations. This leads to finding x = 2.2, and consequently y = -1.4. Therefore, the solution set is (2.2, -1.4). For question 2, the equations yield a solution of (1.33, 1).
Answer:
Yes, the cost 
in dollars and the quantity of yogurt 
are indeed proportional.
The relationship can be expressed as: 
Step-by-step explanation:
1. If varies directly with , it can be represented as:
Here, 
represents the constant of proportionality.
2. We'll calculate the proportionality constant. Given that 
and 
, we have:
3. Thus, the equation becomes:
4. Now, we need to verify proportionality. Substituting 
, which is the quantity of yogurt purchased by Jonah, we should arrive at $0.48:
5. They are indeed directly proportional.
Examining Talia's steps to derive the line equation, we identify the erroneous step as detailed below:
Step 1:
Select a point on the line, such as (2,5)
Step 2:
<span>Select another point on the line, such as (1, 3)
Step 3:
</span><span>Measure units to find the slope. The line moves 1 unit to the right and 2 units upward, resulting in a slope of
(5-3)/(2-1) = 2/1 = 2
Step 4:
</span><span>Apply these values in the point-slope form
y - y1 = m(x - x1)
y - 3 = 2(x - 1)
y = 2x + 1
Hence, the conclusion is:
</span><span>Step 4 is erroneous due to incorrect application of (1, 3) in the point-slope format.</span>
