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In this lesson, we will learn how to find the equation of a line through two points and how to express the equation in different forms.

Q1:

A line πΏ passes through the points ( 3 , 3 ) and ( β 1 , 0 ) . Work out the equation of the line, giving your answer in the form π π¦ + π π₯ + π = 0 .

Q2:

A line πΏ passes through the points ( 2 , 3 ) and ( β 2 , 5 ) . Work out the equation of the line, giving your answer in the form π¦ = π π₯ + π .

Q3:

A line πΏ passes through the points ( 1 , 1 ) and ( β 5 , β 1 ) . Work out the equation of the line, giving your answer in the form π¦ = π π₯ + π .

Q4:

Let π΄ be the point ( 5 , β 1 ) and π΅ be the point ( β 1 , 8 ) . Which of the following points is on β ο© ο© ο© ο© β π΄ π΅ ?

Q5:

What is the equation of the function seen in the given graph?

Q6:

The following graph shows the money that Scarlett earns.

Write an equation to represent the relationship between dollars and time.

Q7:

Find the equation that represents the relation between π₯ and π¦ .

Q8:

The line through points ( 3 , β 3 ) and ( 8 , 1 ) has equation π¦ = π π₯ β 4 . What is π ?

Q9:

Suppose that π΄ π΅ is a chord of a circle π , π· is the midpoint of π΄ π΅ , and the coordinates of π΄ and π΅ are ( 1 , 4 ) and ( 3 , 5 ) . Find the equation of β ο© ο© ο© ο© ο© ο© β π π· .

Q10:

Determine the equation of the straight line given in the diagram.

Q11:

A line πΏ passes through the points ( β 2 , 4 ) and ( 4 , β 3 ) . Work out the equation of the line, giving your answer in the form π¦ = π π₯ + π .

Q12:

A line πΏ passes through the points ( β 1 , 2 ) and ( 3 , 6 ) . Work out the equation of the line, giving your answer in the form π¦ = π π₯ + π .

Q13:

Given that the points ( β 1 , β 4 ) , ( 3 , π¦ ) , and ( β 5 , β 6 ) are collinear, find the value of π¦ .

Q14:

Find the equation of the straight line which passes through the two points ( β 1 , β 2 ) and ( β 7 , β 4 ) .

Q15:

Find the equation of the straight line which passes through the two points ( 1 , 4 ) and ( 5 , 6 ) .

Q16:

Find the equation of the straight line which passes through the two points ( β 1 , 2 ) and ( 3 , β 4 ) .

Q17:

Find the equation of the straight line which passes through the two points ( β 2 , β 3 ) and ( 4 , 7 ) .

Q18:

If π΄ π΅ πΆ π· is a square in which π΄ ( 8 , 1 ) and πΆ ( β 3 , 5 ) , find the equation of β ο© ο© ο© ο© β π΅ π· in the form of π¦ = π π₯ + π .

Q19:

In the figure shown, points π΄ and π΅ have coordinates ( 8 , 0 ) and οΌ 0 , β 5 2 ο . Determine πΆ and then the equation of the line β ο© ο© ο© ο© β π΄ πΆ .

Q20:

Determine, in the form π¦ = π π₯ + π , the equation of the axis of symmetry of π΄ π΅ , where the coordinates of π΄ and π΅ are ( β 3 , 4 ) and ( 1 , 5 ) respectively.

Q21:

Find the linear equation that includes the two points (2, 3) and (0, 6).

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