Question

1. write the a… -intercept form of the equation for the line passing through the point (-4, -1) and having slope \\(\frac{1}{7}\\).

a. \\(y = \frac{1}{7}x - \frac{3}{7}\\)
b. \\(y = -\frac{1}{7}x - 1\frac{6}{7}\\)
c. \\(y = \frac{1}{7}x + \frac{7}{3}\\)
d. \\(y = 7x - 21\\)

1. a local fair charges an entry fee as well as a fee for each ride ticket purchased at the fair. the equation \\(y = 3x + 15\\) can be used to determine the amount of money a person will spend at the fair.

what do the numbers 3 and 15 represent in terms of money spent at the local fair?
a. the 3 represents the cost per ticket, and the 15 represents the entry fee.
b. the 3 represents the entry fee, and the 15 represents the cost per ticket.
c. the 3 represents the entry fee, and the 15 represents the total amount paid.
d. the 3 represents the cost per ticket, and the 15 represents the total amount paid.

1. eric planted a seedling in his garden and recorded its height each week. the equation shown can be used to estimate the height, \\(h\\), in inches, of the seedling by the end of each week, \\(w\\), after it was planted.

what does the slope of the graph of the equation \\(h = \frac{3}{4}w + \frac{9}{4}\\) represent?
a. the height, in inches, of the seedling after \\(w\\) weeks
b. the height, in inches of the seedling when eric first planted it
c. the increase in the height, in inches, of the seedling each week
d. the total increase in the height, in inches, of the seedling after \\(w\\) weeks

1. lamar starts his own painting business. he pays for some supplies to begin, and then charges a fixed amount per room. the graph shows a linear function that models lamar’s profit per room.

graph of a linear function with x-axis (rooms) and y-axis (profit)
what does the initial value represent?
a. the number of rooms he paints
b. the amount he charges per room
c. the amount he spends in supplies
d. the amount of profit he makes per room

Answer:

Question 33

To find the equation of the line in slope - intercept form \(y = mx + b\) (where \(m\) is the slope and \(b\) is the y - intercept) passing through the point \((-4,-1)\) with slope \(\frac{1}{7}\):

Step 1: Use the point - slope form

The point - slope form of a line is \(y - y_1=m(x - x_1)\), where \((x_1,y_1)=(-4,-1)\) and \(m = \frac{1}{7}\).
Substitute the values into the formula: \(y-(-1)=\frac{1}{7}(x - (-4))\)
Simplify: \(y + 1=\frac{1}{7}(x + 4)\)

Step 2: Convert to slope - intercept form

Expand the right - hand side: \(y+1=\frac{1}{7}x+\frac{4}{7}\)
Subtract 1 from both sides. Since \(1=\frac{7}{7}\), we have \(y=\frac{1}{7}x+\frac{4}{7}-\frac{7}{7}\)
Simplify the right - hand side: \(y=\frac{1}{7}x-\frac{3}{7}\)? Wait, no, wait. Wait, the options have \(y=\frac{1}{7}x+\frac{7}{3}\)? Wait, maybe I made a mistake. Wait, let's re - calculate.

Wait, the slope is \(\frac{1}{7}\), point \((-4,-1)\)

Using \(y=mx + b\), substitute \(x=-4\), \(y = - 1\) and \(m=\frac{1}{7}\) into \(y=mx + b\):

\(-1=\frac{1}{7}\times(-4)+b\)

\(-1=-\frac{4}{7}+b\)

Add \(\frac{4}{7}\) to both sides: \(b=-1+\frac{4}{7}=-\frac{7}{7}+\frac{4}{7}=-\frac{3}{7}\)? But the option c is \(y = \frac{1}{7}x+\frac{7}{3}\), option a is \(y=\frac{1}{7}x-\frac{3}{7}\). Wait, maybe there is a typo in the problem or my mis - reading. Wait, if the slope is \(\frac{1}{7}\) and the point is \((-4,-1)\), then:

\(y+1=\frac{1}{7}(x + 4)\)

\(y=\frac{1}{7}x+\frac{4}{7}-1=\frac{1}{7}x+\frac{4 - 7}{7}=\frac{1}{7}x-\frac{3}{7}\), which is option a? But the original problem's option a is \(y=\frac{1}{7}x-\frac{3}{7}\)? Wait, the user's image shows option a as \(y=\frac{1}{7}x-\frac{3}{7}\)? Wait, maybe I mis - read the slope. Wait, the problem says "slope \(\frac{1}{7}\)"? Wait, maybe the slope is \(\frac{1}{7}\), then the correct answer is a. \(y=\frac{1}{7}x-\frac{3}{7}\)

Question 34

The equation is \(y = 3x+15\), which is in the form \(y=mx + b\), where \(x\) is the number of ride tickets.

In the context of a fair, the entry fee is a fixed cost (the y - intercept, when \(x = 0\), \(y = 15\)), and the cost per ticket is the slope (the rate of change, \(m = 3\)).

So, 3 represents the cost per ticket and 15 represents the entry fee. So the answer is a. The 3 represents the cost per ticket, and the 15 represents the entry fee.

Question 35

The equation is \(h=\frac{3}{4}w+\frac{9}{4}\), which is in the form \(y = mx + b\) (here \(h\) is like \(y\), \(w\) is like \(x\)).

The slope \(m=\frac{3}{4}\) in the equation \(y=mx + b\) represents the rate of change of \(y\) with respect to \(x\). In the context of the seedling's height, the slope represents the increase in height per week.

So the slope \(\frac{3}{4}\) represents the increase in the height, in inches, of the seedling each week. The answer is c.

Question 36

The graph models Lamar's profit per room. The initial value (the y - intercept, when the number of rooms \(x = 0\)) represents the profit when he has painted 0 rooms. Since he has to pay for supplies to begin, when \(x = 0\) (no rooms painted), the profit will be negative (or represent the cost of supplies). The initial value (y - intercept) represents the amount he spends on supplies (because when \(x = 0\) (no rooms painted), his profit is affected by the supply cost).

So the answer is c. The amount he spends in supplies.

Final Answers

1. a. \(y=\frac{1}{7}x-\frac{3}{7}\)

1. a. The 3 represents the cost per ticket, and the 15 represents the entry fee.

1. c. the increase in the height, in inches, of the seedling each week

1. c. The amount he spends in supplies