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In this lesson, we will learn how to find the equation of a straight line that is either horizontal, parallel, or perpendicular to another line.

Q1:

Which of the following lines is perpendicular to the line 1 9 π₯ β 3 π¦ = 5 ?

Q2:

Lines π΄ and π΅ are perpendicular to each other and meet at ( 1 , 4 ) . If the slope of π΄ is 3 2 , what is the equation of line π΅ ?

Q3:

Consider the graph:

Which of the following could be the equation of the line?

Q4:

Which axis is the straight line π¦ = 3 parallel to?

Q5:

Write, in the form π¦ = π π₯ + π , the equation of the line that is perpendicular to the line β 5 π₯ + 2 π¦ = β 6 and that intercepts the π₯ -axis at 20.

Q6:

Write, in the form π¦ = π π₯ + π , the equation of the line through π΄ ( 5 , β 8 ) that is perpendicular to π΄ π΅ , where π΅ ( β 8 , β 3 ) .

Q7:

In the figure below, πΏ β«½ πΏ 1 2 and π΄ π΅ = 8 length units. If the equation of πΏ 1 is π¦ = 4 5 π₯ + 4 , find the equation of πΏ 2 .

Q8:

Find the equation of the straight line passing through the point ( β 1 , 1 ) and perpendicular to the straight line passing through the points ( β 9 , 9 ) and ( 6 , β 3 ) .

Q9:

If the straight line passing through the two points ( 2 , 8 ) and ( 3 , 3 ) is perpendicular to the straight line whose equation is 3 π₯ + π π¦ + 8 = 0 , find the value of π .

Q10:

If the two straight lines πΏ βΆ β 8 π₯ + 7 π¦ β 9 = 0 1 and πΏ βΆ π π₯ + 2 4 π¦ + 5 6 = 0 2 are perpendicular, find the value of π .

Q11:

The straight lines 8 π₯ + 5 π¦ = 8 and 8 π₯ + π π¦ = β 8 are parallel. What is the value of π ?

Q12:

The line π¦ = ( π + 5 ) π₯ β 6 is perpendicular to the line through points ( β 8 , 2 ) and ( β 2 , 5 ) . What is π ?

Q13:

The square π΄ π΅ πΆ π· has an area of 13, and the corner π΅ has coordinates ( 2 , 1 ) . Give the equation of β ο© ο© ο© ο© β πΆ π in the form π¦ = π π₯ + π .

Q14:

Given π΄ ( 4 , 4 ) and π΅ ( 2 , β 4 ) , find the equation of the perpendicular to π΄ π΅ that passes through the midpoint of this line segment. Give your answer in the form π¦ = π π₯ + π .

Q15:

The line 4 π₯ β 3 π¦ β 2 4 = 0 meets the π₯ - and π¦ -axis at points π΄ and π΅ respectively. Find the equation of the line perpendicular to π΄ π΅ and passing through its midpoint.

Q16:

Given π΄ ( 2 , β 7 ) and π΅ ( β 8 , 1 ) , what is the perpendicular bisector of the segment π΄ π΅ ?

Q17:

Let π΄ and π΅ be the π₯ - and π¦ -intercepts of the line 5 π₯ β 3 π¦ β 6 = 0 . Give the equation of the line parallel to the π¦ -axis that passes through the midpoint of π΄ π΅ .

Q18:

Which axis is the straight line β π = ( 2 , 5 ) + πΎ ( 0 , 1 ) parallel to?

Q19:

If lines π¦ = π π₯ + π and π¦ = π π₯ + π are perpendicular, which of the following products equals β 1 ?

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