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In this lesson, we will learn how to find the general and vector forms of the equation of a straight line passing through the point of intersection of two lines.

Q1:

Find the equation of the line perpendicular to β 6 π₯ β π¦ + 8 = 0 and passing through the intersection of the lines β 4 π₯ β π¦ β 3 = 0 and β 3 π₯ + 8 π¦ β 1 = 0 .

Q2:

What is the equation of the line passing through π΄ ( β 1 , 3 ) and the intersection of the lines 3 π₯ β π¦ + 5 = 0 and 5 π₯ + 2 π¦ + 3 = 0 ?

Q3:

What is the equation of the line passing through π΄ ( β 3 , 5 ) and the intersection of the lines 4 π₯ + 2 π¦ + 1 = 0 and 2 π₯ + 3 π¦ β 2 = 0 ?

Q4:

What is the equation of the line passing through π΄ ( 2 , β 1 ) and the intersection of the lines 2 π₯ + π¦ β 4 = 0 and 2 π₯ β 4 π¦ β 1 = 0 ?

Q5:

Find the equation of the straight line that is parallel to the π¦ -axis and passes through the point of intersection of the two straight lines π¦ = β 3 and π₯ = 1 1 1 5 π¦ .

Q6:

Find the equation of the straight line that is parallel to the π¦ -axis and passes through the point of intersection of the two straight lines π¦ = 9 and π₯ = β 5 2 π¦ .

Q7:

The function π ( π₯ ) is represented by the line β ο© ο© ο© ο© β π΄ π΅ and the function π ( π₯ ) is represented by the line β ο© ο© ο© ο© ο© β π π΄ where the coordinates of π΄ are ( 2 , 5 ) . Find the equations of π ( π₯ ) and π ( π₯ ) .

Q8:

Find the equation of the straight line that passes through the origin and the point of intersection of the two straight lines π₯ = β 1 7 4 and π¦ = β 5 .

Q9:

Find the equation of the straight line that passes through the origin and the point of intersection of the two straight lines π₯ = 1 4 and π¦ = β 8 7 .

Q10:

Find the equation of the vector that is parallel to the π¦ -axis and passes through the point of intersection of the two straight lines β π = π ( β 6 , β 4 ) and β 3 π₯ + 5 π¦ = β 5 .

Q11:

Find the π₯ -coordinate of the point at which the straight line 3 π₯ + 9 π¦ = 0 cuts the π₯ -axis.

Q12:

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

Q13:

Find the equation of the straight line that passes through the point of intersection of the two straight lines π₯ β 8 π¦ = 2 and β 6 π₯ β 8 π¦ = 1 and parallel to the π¦ -axis.

Q14:

Find the equation of the straight line that passes through the point of intersection of the two straight lines 2 π₯ β 2 π¦ = 1 and β π₯ + 3 π¦ = β 8 and parallel to the π¦ -axis.

Q15:

Find the equation of the straight line which passes through the point of intersection of the two lines β 4 π₯ + 1 5 π¦ = β 1 5 and β 4 π₯ + 3 π¦ = 1 4 and is parallel to the straight line β π = ( 4 , 0 ) + π ( 5 , β 4 ) .

Q16:

Find the equation of the straight line which passes through the point of intersection of the two lines β 1 3 π₯ β 5 π¦ = 1 4 and 2 π₯ + 1 5 π¦ = β 1 1 and is parallel to the straight line π₯ + 8 π¦ = β 1 4 .

Q17:

Determine the equation of the line passing through the point of intersection of the two lines whose equations are 5 π₯ + 2 π¦ = 0 and 3 π₯ + 7 π¦ + 1 3 = 0 while making an angle of 1 3 5 β with the positive π¦ -axis.

Q18:

Determine the equation of the line passing through the point of intersection of the two lines whose equations are 2 π₯ β π¦ β 7 = 0 and π₯ + 2 π¦ β 6 = 0 while making an angle of 4 5 β with the positive π¦ -axis.

Q19:

Find the vector equation of the straight line that passes through the point of intersection of the two straight lines β 8 π₯ β π¦ = 7 and β 5 π₯ β 3 π¦ = 2 and the point ( 1 2 , 8 ) .

Q20:

Find the vector equation of the straight line that passes through the point of intersection of the two straight lines 5 π₯ + π¦ = 6 and 2 π₯ + 1 3 π¦ = 1 5 and the point ( 0 , β 9 ) .

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