Art and his friends spent $62 at the movies. Admission tickets cost $12 apiece, and a bucket of popcorn costs $7. Which equation written in standard form represents the number of tickets bought, t, and the number of buckets of popcorn bought, p?

1. **Which equation written in standard form represents the number of tickets bought, t, and the number of buckets of popcorn bought, p?**

To formulate the correct equation, let's set \( t \) as the number of tickets and \( p \) as the number of popcorn buckets. The cost of tickets is \( 12t \) and the cost of popcorn is \( 7p \). The total spending is \( 62 \). Therefore, the equation can be stated as:
\[ 12t + 7p = 62 \]

So the answer is: **7p + 12t = 62.**

2. **What is the equation of the graphed line written in standard form?**

For a vertical line passing through x = -3, the equation is simply:
\[ x = -3 \]

So the answer is: **x = -3.**

3. **What is the x-intercept of the graph of the equation x + 2y = 5?**

To find the x-intercept of the equation \( x + 2y = 5 \), set \( y = 0 \):
\[ x + 2(0) = 5 \Rightarrow x = 5. \]

So the answer is: **5.**

4. **What is the equation of the graphed line passing through (-3, 0), (0, -2), and (3, -4) written in standard form?**

First, find the slope using any two points (let’s use (-3, 0) and (0, -2)):
Slope \( m = \frac{-2 - 0}{0 - (-3)} = \frac{-2}{3}. \)

Using point-slope form \( y - y_1 = m(x - x_1) \), we can use point (0, -2):
\[ y + 2 = -\frac{2}{3}x \]
Multiply by 3 to eliminate fractions:
\[ 3y + 6 = -2x \]
Rearranging gives us:
\[ 2x + 3y = -6. \]

So the answer is: **2x + 3y = -6.**

5. **Which is the equation of the graphed line written in standard form passing through (-4, -4), (0, 0), and (4, 4)?**

The points (0, 0) show it's the origin. The slope between these points is 1 (therefore the line is y = x). In standard form, this can be rearranged to:
\[ x - y = 0. \]

So the answer is: **y = x.**

6. **What is the slope of the line 4x - 2y = 5?**

To find the slope, we can rearrange the equation to slope-intercept form (\(y = mx + b\)):
\[ -2y = -4x + 5 \]
\[ y = 2x - \frac{5}{2} \]
The slope \( m \) is \( 2 \).

So the answer is: **2.**

7. **What is the equation of the graphed line passing through (0, -4) and (2, 0) written in standard form?**

The slope using the two points is given by \( m = \frac{0 - (-4)}{2 - 0} = \frac{4}{2} = 2 \).
Using point-slope form at point (0, -4):
\[ y + 4 = 2(x - 0) \]
Multiply to get:
\[ y = 2x - 4 \]
Rearranged to standard form gives:
\[ 2x - y = 4. \]

So the answer is: **2x - y = 4.**

8. **What is the x-intercept of the curve described by the equation 2x - 3y = 12?**

To find the x-intercept, set \( y = 0 \):
\[ 2x - 3(0) = 12 \]
\[ 2x = 12 \Rightarrow x = 6. \]

So the answer is: **6.**

9. **What is the slope of the line 3x - 9y = 4?**

Rearranging to slope-intercept form:
\[ -9y = -3x + 4 \]
Divide by -9:
\[ y = \frac{1}{3}x - \frac{4}{9} \]
So the slope \( m = \frac{1}{3} \).

So the answer is: **StartFraction one-third EndFraction.**

10. **What is the graph of 3x + 5y = -15?**

To find the intercepts:
- **x-intercept:** Set \( y = 0 \):
\[ 3x = -15 \Rightarrow x = -5. \]

- **y-intercept:** Set \( x = 0 \):
\[ 5y = -15 \Rightarrow y = -3. \]

Therefore, the graph passes through (-5, 0) and (0, -3). So the answer is: **A coordinate plane with a line passing through (negative 5, 0) and (0, negative 3).**

for 10 graph 1 2 3 or 4? A coordinate plane with a line passing through (negative 5, 0) and (3, 0).A coordinate plane with a line passing through (0, 3) and (5, 0).A coordinate plane with a line passing through (negative 5, 0) and (0, 3).A coordinate plane with a line passing through (0, negative 3) and (5, 0).

To clarify the graph of the line defined by the equation \(3x + 5y = -15\):

1. **Find the x-intercept**:
Set \(y = 0\):
\[
3x + 5(0) = -15 \implies 3x = -15 \implies x = -5.
\]
So the x-intercept is at the point \((-5, 0)\).

2. **Find the y-intercept**:
Set \(x = 0\):
\[
3(0) + 5y = -15 \implies 5y = -15 \implies y = -3.
\]
So the y-intercept is at the point \((0, -3)\).

From the intercepts, we have the points \((-5, 0)\) for the x-intercept and \((0, -3)\) for the y-intercept.

Now, looking at your options for the graph:

1. A coordinate plane with a line passing through (negative 5, 0) and (3, 0).
2. A coordinate plane with a line passing through (0, 3) and (5, 0).
3. A coordinate plane with a line passing through (negative 5, 0) and (0, 3).
4. A coordinate plane with a line passing through (0, negative 3) and (5, 0).

The correct description for the line represented by \(3x + 5y = -15\) is:
**A coordinate plane with a line passing through (negative 5, 0) and (0, negative 3).**

However, since this exact option is not listed, the closest match would be:
- A coordinate plane with a line passing through (negative 5, 0) and (0, negative 3).

If you have an option that directly reflects the y-intercept at (0, -3), that would confirm it as well! Otherwise, none of the listed options perfectly fit the description.

thats the exact same phrasing?? what graph tho 1 2 3 or 4?1. A coordinate plane with a line passing through (negative 5, 0) and (3, 0). 2. A coordinate plane with a line passing through (0, 3) and (5, 0). 3. A coordinate plane with a line passing through (negative 5, 0) and (0, 3). 4. A coordinate plane with a line passing through (0, negative 3) and (5, 0).

I apologize for any confusion in my previous response. Based on the calculation of the intercepts for the equation \(3x + 5y = -15\):

- **x-intercept** is \((-5, 0)\).
- **y-intercept** is \((0, -3)\).

Now, we can match these points to your options:

1. **A coordinate plane with a line passing through (negative 5, 0) and (3, 0)**: This doesn't match because it suggests another point on the x-axis (3, 0) which isn't correct.

2. **A coordinate plane with a line passing through (0, 3) and (5, 0)**: This is incorrect as it suggests points not related to the ones we calculated.

3. **A coordinate plane with a line passing through (negative 5, 0) and (0, 3)**: This is incorrect because it includes (0, 3) instead of (0, -3).

4. **A coordinate plane with a line passing through (0, negative 3) and (5, 0)**: This is not correct because it includes (5, 0) which is not an intercept for this line.

**The correct graph features the points (-5, 0) and (0, -3)**, but since that option is not listed among your choices, based on your options alone, **Option 1 (the only one that includes the correct x-intercept)** with an incorrect point (3, 0) doesn't properly reflect the line's behavior.

So, there isn't a perfect match from the provided options, because none include both known points. If you're specifically looking for the closest match based solely on the information given:

Choose **Option 1** as it has the correct x-intercept.

5. x – y = 0 otherwise yay!

Great! It sounds like you've got a handle on these problems.

For **Question 5**, you mentioned the equation \(x - y = 0\), which indeed represents a line that passes through the origin (0,0) with a slope of 1, or simply \(y = x\). This means any point on the line has equal x and y values, including the points (0, 0), (1, 1), (-1, -1), etc.

If you have any more questions or if there's anything else you'd like to go over, feel free to reach out!