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In this lesson, we will learn how to find the equation of a straight line in different forms given its slope and its y-intercept.

Q1:

Write the equation represented by the graph shown. Give your answer in the form π₯ + π¦ = π .

Q2:

Which equation represents the line shown?

Q3:

In the figure below, is the point and . Find the coordinates of , the gradient of , and the equation of the perpendicular to that passes through in the form .

Q4:

Write the equation represented by the graph shown. Give your answer in the form π¦ = π π₯ + π .

Q5:

The graph of the equation π¦ + 2 = 5 ( π₯ + 1 ) is a straight line.

What is the slope of the line?

Which one of the following points lies on the line?

Q6:

Find the coordinates of the point where π¦ = 4 π₯ + 1 2 intersects the π¦ -axis.

Q7:

Find the coordinates of the point where π¦ = 3 π₯ + 9 intersects the π¦ -axis.

Q8:

Which of the following graphs represents the equation π¦ = β 5 π₯ β 2 ?

Q9:

Does the point ( 4 , β 1 1 ) lie on the line π¦ = β 2 π₯ β 4 ?

Q10:

The line π₯ β 2 β 5 = π¦ β 2 β 7 = π§ β 1 β 1 0 passes through the sphere π₯ + π¦ + π§ β 1 8 π₯ + 8 π¦ + 1 4 π§ + 2 8 = 0 2 2 2 . Find the length of the line segment between the two points of intersection of the line and the sphere. Give your answer to the nearest hundredth.

Q11:

Find the equation of the line with π₯ -intercept 3 and π¦ -intercept 7, and calculate the area of the triangle on this line and the two coordinate axes.

Q12:

Find the equation of the line with π₯ -intercept 4 and π¦ -intercept 9, and calculate the area of the triangle on this line and the two coordinate axes.

Q13:

Find the equation of the line with π₯ -intercept 3 and π¦ -intercept 5, and calculate the area of the triangle on this line and the two coordinate axes.

Q14:

Find the coordinates of the -intercept and the gradient of the straight line whose equation is .

Q15:

Does the point ( 2 , β 3 ) lie on the line π¦ = 5 π₯ β 7 ?

Q16:

Does the point οΌ 1 , β 9 2 ο lie on the line π¦ = 1 2 π₯ β 5 ?

Q17:

Find the equation, in the form , of the line with gradient and -intercept .

Q18:

Which of the following graphs represents the equation π¦ = 2 π₯ 3 β 2 ?

Q19:

What is the slope of the line that passes through the point ( 4 , 1 8 ) and intercepts π¦ at β 2 ?

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