1. The line AC intersects the x-axis at the point (4,0)A.

The line 18 = y intersects the line AC at point C.

The point B is the point of intersection of the straight line AC with the axis of the p.

Given 8 = CD .tone

A. Find the equation of the line AC.

on. Prove: ACDB - AAOB and calculate the similarity ratio.

The line y = t( is a number) intersects the line AC

at the point , so that EM = CD holds (see diagram).

third. Add the appropriate sign from these signs to the claims:

~, (similar, overlaps), and reasoned:

ACDB

DAOB

DMEB

DMEB

d. What is the equation of the straight line EM? Nemko

The problem provided involves a geometric setup with a line \( AC \) intersecting the x-axis and y-axis, along with points of intersection and some calculations related to line equations and similarity of triangles.

### Given Information:
1. **Line AC**: 
   - Intersects the x-axis at \( (4,0) \).
   - Intersects the line \( y = 18 \) at point \( C \).
   - Point \( B \) is the intersection of line \( AC \) with the p-axis.
   
2. **Additional Points**:
   - \( 8 = CD \) (This could be a given distance, but the context isn't fully clear).
   - The line \( y = t \) intersects line \( AC \) at a point such that \( EM = CD \).
   
3. **Tasks**:
   - Find the equation of line \( AC \).
   - Prove that triangles \( ACDB \) and \( AAOB \) are similar and calculate the similarity ratio.
   - Solve for other relationships involving the points \( DMEB \) and find the equation of line \( EM \).

### Step 1: Equation of Line AC
The line intersects the x-axis at \( A(4,0) \) and the y-axis at \( C \). To find the equation of a line, we typically use the slope-intercept form:
\[
y = mx + c
\]
Where \( m \) is the slope and \( c \) is the y-intercept.

Given:
- Point \( A(4,0) \) lies on the x-axis.
- Point \( C \) lies on the y-axis where \( y = 18 \).

If we find the slope \( m \) using the coordinates of points \( A \) and \( C \), we can determine the equation of the line.

### Step 2: Prove Similarity of Triangles
To prove that triangles \( ACDB \) and \( AAOB \) are similar, we would need to show that the corresponding angles are equal, or the corresponding sides are proportional.

### Step 3: Equation of Line EM
The equation of line \( EM \) would depend on the coordinates of points \( E \) and \( M \), and we would solve this using the slope-intercept form again, once the coordinates are identified.

### Clarifications and Next Steps
Please clarify or confirm details, such as the exact coordinates of points \( B \) and \( D \), or additional conditions that may not be fully described in the problem statement.

Would you like to proceed with finding the equation of line \( AC \) and solving the similarity proof? Let me know!

Explore the solution to a geometric problem involving the intersection of line AC, calculation of triangle similarity between ACDB and AAOB, and finding the equation of line EM. This problem covers key concepts in geometry and triangle similarity theorems.

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