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The image you uploaded contains five business mathematics questions, which I'll now solve step by step.

### Question 1:
Find the demand function passing through points (3,3) and (2,4).

We need to determine the equation of the line passing through the given points. Using the slope formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 3}{2 - 3} = -1
\]

Now, using the point-slope form of a line equation:

\[
y - y_1 = m(x - x_1)
\]

Choose point (3,3):

\[
y - 3 = -1(x - 3) \implies y = -x + 6
\]

Thus, the demand function is **P = -x + 6** (Option B).

---

### Question 2:
Find the intercept of the following equations:
\(Y = 2 + 2x\) and \(Y = 10 - 2x\).

We set the two equations equal to find their intersection:

\[
2 + 2x = 10 - 2x
\]

Solving for \(x\):

\[
4x = 8 \implies x = 2
\]

Substitute \(x = 2\) into either equation (use \(Y = 2 + 2x\)):

\[
Y = 2 + 2(2) = 6
\]

Thus, the intercept is at point **(2,6)** (Option E).

---

### Question 3:
Find the slope of the line passing through points A(2,8) and B(4,5).

Using the slope formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 8}{4 - 2} = \frac{-3}{2}
\]

Thus, the slope is **-1.5** (Option C).

---

### Question 4:
Find the equation of the line passing through point (4,1) with slope 2.

Using the point-slope form again:

\[
y - y_1 = m(x - x_1)
\]

Substitute \(m = 2\) and point (4,1):

\[
y - 1 = 2(x - 4) \implies y = 2x - 8 + 1 = 2x - 7
\]

Thus, the equation is **Y = 2x - 7** (Option C).

---

### Question 5:
Find the slope of the line \(Y = ax + 2\) parallel to the line passing through points (2,4) and (3,1).

First, find the slope of the line passing through (2,4) and (3,1):

\[
m = \frac{1 - 4}{3 - 2} = -3
\]

Since the two lines are parallel, the slope of \(Y = ax + 2\) must also be **-3** (Option A).

---

### Would you like further details on any of the solutions? 

Here are five related questions:
1. How do you determine the equation of a line given two points?
2. What is the importance of slopes in linear equations?
3. How do parallel lines relate in terms of slope?
4. What are the different forms of a linear equation?
5. How do you find the point of intersection of two lines?

**Tip**: When working with equations of lines, always remember the slope-intercept form, \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

The image contains five business mathematics questions on topics such as finding demand functions, determining intercepts, calculating slopes, and writing equations of lines.

Solve a business mathematics quiz covering demand functions, intercepts, slopes, and line equations. Includes detailed solutions to problems such as finding equations of lines, calculating slopes between points, and determining intercepts. Suitable for Grades 9-12.

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