# Worksheet: General Equation of a Line through the Intersection Point of Two Lines

In this worksheet, we will practice finding the general and vector forms of the equation of a straight line passing through the point of intersection of two lines.

**Q2: **

Determine the equation of the line passing through the point of intersection of the two lines whose equations are and while making an angle of with the positive -axis.

- A
- B
- C
- D

**Q3: **

Find the equation of the straight line that passes through the origin and the point of intersection of the two straight lines and .

- A
- B
- C
- D

**Q4: **

Find the equation of the straight line that is parallel to the -axis and passes through the point of intersection of the two straight lines and .

- A
- B
- C
- D

**Q5: **

What is the equation of the line passing through and the intersection of the lines and ?

- A
- B
- C

**Q6: **

Find the equation of the straight line that passes through the point of intersection of the two straight lines and and parallel to the -axis.

- A
- B
- C
- D

**Q7: **

Find the equation of the straight line which passes through the point of intersection of the two lines and and is parallel to the straight line .

- A
- B
- C
- D

**Q8: **

Find the equation of the straight line which passes through the point of intersection of the two lines and and is parallel to the straight line .

- A
- B
- C
- D

**Q9: **

Find the equation of the vector that is parallel to the -axis and passes through the point of intersection of the two straight lines and .

- A
- B
- C
- D

**Q10: **

Find the vector equation of the straight line that passes through the point of intersection of the two straight lines and and the point .

- A
- B
- C
- D

**Q11: **

Find the -coordinate of the point at which the straight line cuts the -axis.

- A3
- B9
- C
- D0

**Q12: **

Which of the following equations represents a line through the origin?

- A
- B
- C
- D

**Q13: **

The function is represented by the line and the function is represented by the line where the coordinates of are . Find the equations of and .

- A ,
- B ,
- C ,
- D ,
- E ,

**Q14: **

The lines and intersect orthogonally. Find the coordinates of the point of intersection.

- A
- B
- C
- D

**Q15: **

Find the equation of the straight line that passes through the point of intersection of the two lines and , given that it is perpendicular to the second line.

- A
- B
- C
- D

**Q16: **

Find the point of intersection of the two straight lines and .

- A
- B
- C
- D

**Q17: **

Find the equation of the straight line that passes through the point of intersection of the two straight lines and and intersects the negative direction of the -axis at a point that is 10 length units away from the origin.

- A
- B
- C
- D

**Q18: **

Determine the point of intersection of the two straight lines represented by the equations and .

- A
- B
- C
- D

**Q19: **

Find the equation of the straight line, passing through the point of intersection of the two straight lines and , that intersects the positive directions of the coordinate axes in two points at the same distance from the origin.

- A
- B
- C
- D

**Q20: **

What is the equation of the line passing through and the intersection of the lines and ?

- A
- B
- C