In this worksheet, we will practice calculating 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.

**Q3: **

What is the value of so that , , and are collinear?

**Q4: **

Given that and are the direction vectors of two perpendicular straight lines, determine the value of .

- A
- B
- C
- D72

**Q5: **

In the square with and , the diagonals are and . What is the slope of ?

- A6
- B
- C0
- D1

**Q6: **

Determine the slope of the straight line that makes an angle whose cosine is with the positive -axis.

- A
- B
- C
- D

**Q7: **

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

**Q8: **

If is a parallelogram, where and , find the slope of .

- A
- B
- C
- D

**Q9: **

Given that is right angled at and that the coordinates of and are and , respectively, determine the slope of .

- A
- B
- C0
- D

**Q10: **

Find the slope of the straight line whose equation is and passes through the point .

- A
- B
- C
- D

**Q11: **

In this figure, the slope of is .

- Aundefined
- Bzero
- Cpositive
- Dnegative

**Q12: **

Given that the slope of the line passing through , , and is , find the values of and .

- A ,
- B ,
- C ,
- D ,
- E ,

**Q13: **

Find the slope of the given straight line.

- A
- B
- C7
- D
- E1

**Q14: **

is a right-angled triangle at where and the coordinates of and are and respectively. Find the coordinates of given the slope of is 1.

- A
- B
- C
- D
- E

**Q15: **

Use the graph to answer the following questions.

Determine the lengths of , , , and .

- A , , ,
- B , , ,
- C , , ,
- D , , ,
- E , , ,

What is the ratio of ?

What do you notice about the ratios and ?

- AThey are not equal.
- BThey are equal.

What do the ratios and represent?

- Athe inverse of the slope of the line
- Bthe slope of the line

**Q16: **

Which line has a slope that is greater than 1?

- A b
- B a
- C c

**Q19: **

Which of the following characteristics does the line that passes through the points , , and have?

- A a positive slope and a negative -intercept
- B a positive slope and a positive -intercept
- C a negative slope and a positive -intercept
- Da negative slope and a negative -intercept

**Q20: **

What is the value of 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 . 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.

- A2, decreasing
- B3, decreasing
- C1.5, increasing
- D , decreasing

**Q24: **

Suppose that a line has direction vector . What, to the nearest second, is the measure of the positive angle that this line makes with the positive -axis?

- A
- B
- C
- D