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In this lesson, we will learn how to calculate the slope of a line given two points that lie on it and find the coordinates of a point on a line where another point and the slope are known.

Q1:

Line 1 passes through point π΄ ( β 6 , 1 7 ) and point π΅ ( β 1 8 , β 1 4 ) and Line 2 passes through the points πΆ ( β 1 2 , 1 8 ) and π· ( β 9 , 2 0 ) . Which of the two lines has a steeper slope?

Q2:

Determine the slope of the line that passes through the points π΄ ( 2 , β 5 ) and π΅ ( 4 , 5 ) .

Q3:

What is the value of π¦ so that π΄ ( β 9 , 6 ) , π΅ ( 3 , β 3 ) , and πΆ ( β 1 , π¦ ) are collinear?

Q4:

Given that ( 9 , 1 ) and ( β 8 , π ) are the direction vectors of two perpendicular straight lines, determine the value of π .

Q5:

In the square π΄ π΅ πΆ π· with π΄ ( β 2 , 3 ) and π΅ ( β 8 , 9 ) , the diagonals are π΄ πΆ and π΅ π· . What is the slope of β ο© ο© ο© ο© β π΅ π· ?

Q6:

Determine the slope of the straight line that makes an angle whose cosine is β 3 4 with the positive π₯ -axis.

Q7:

In the figure below, find the slope of the line πΏ , and round the result to the nearest hundredth.

Q8:

If π΄ π΅ πΆ π· is a parallelogram, where π΄ ( 8 , 2 ) and π΅ ( β 4 , 7 ) , find the slope of β ο© ο© ο© ο© β π· πΆ .

Q9:

Given that β³ π΄ π΅ πΆ is right angled at π΅ and that the coordinates of π΄ and π΅ are ( β 3 , β 8 ) and ( 3 , 0 ) , respectively, determine the slope of β ο© ο© ο© ο© β π΅ πΆ .

Q10:

Find the slope of the straight line whose equation is 6 π¦ = π π₯ + 9 and passes through the point π΄ ( 7 , β 2 ) .

Q11:

In this figure, the slope of β ο© ο© ο© ο© β π΄ π΅ is .

Q12:

Given that the slope of the line passing through ( β 2 , 7 ) , ( π₯ , 3 ) , and ( 5 , π¦ ) is β 1 , find the values of π₯ and π¦ .

Q13:

Find the slope of the given straight line.

Q14:

πΏ π π is a right-angled triangle at πΏ where π β π = 4 5 β and the coordinates of πΏ and π are πΏ ( 7 , β 4 ) and π ( β 3 , β 4 ) respectively. Find the coordinates of π given the slope of π π is 1.

Q15:

Use the graph to answer the following questions.

Determine the lengths of πΉ πΊ , πΊ π» , πΆ π· , and π· πΈ .

What is the ratio of πΊ π» πΉ πΊ ?

What do you notice about the ratios πΊ π» πΉ πΊ and π· πΈ πΆ π· ?

What do the ratios πΊ π» πΉ πΊ and π· πΈ πΆ π· represent?

Q16:

Which line has a slope that is greater than 1?

Q17:

What is the gradient of a line passing through the points and ?

Q18:

True or False: Given a non vertical line, the slopes between any two of its points will be equal.

Q19:

Which of the following characteristics does the line that passes through the points ( β 7 , β 6 . 7 5 ) , ( 3 , β 1 4 . 2 5 ) , and ( β 2 , β 1 0 . 5 ) have?

Q20:

What is the value of π₯ in the graph if the slope is equal to 0.7? Give your answer correct to two decimal places.

Q21:

A straight line has the equation π¦ = 4 π₯ β 5 . What is the slope of the line?

Q22:

Given that a linear function contains the points (2,3) and (0,6), find the slope of the function and state whether it is increasing or decreasing.

Q23:

Given that the slope of a straight line passing through the points ( 9 , β 7 ) and ( β 3 , π ) is β 5 1 2 , find the value of π .

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