The line through (0, 0) and (2, 6) has gradient 3 and the line y = 2x + 5 owns gradient 2 with intercept 5, so this Year 11 sheet reads every line from its equation. The key also records a midpoint answer of (4, 7) and marks parallel lines as a theme.
Key Takeaways
The gradient through (0, 0) and (2, 6) is 3 (Q1).
y = 2x + 5 has gradient 2 and y-intercept 5 (Q2).
The key records a midpoint of (4, 7).
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.What is the gradient of the line through (0, 0) and (2, 6)?
(a) 3(b) 2(c) 6(d) 12
2.Which line has gradient 2 and y-intercept 5?
(a) y = 5x + 2(b) y = 2x + 5(c) y = 2x - 5(d) y = x + 5
3.What is the gradient of the line through (1, 2) and (3, 8)?
(a) 3(b) 2(c) 6(d) 1.5
4.What is the midpoint of the points (2, 4) and (6, 10)?
(a) (4, 7)(b) (8, 14)(c) (3, 6)(d) (4, 6)
5.What is the distance between the points (0, 0) and (6, 8)?
(a) 14(b) 48(c) 10(d) 100
6.The lines y = 2x + 1 and y = 2x - 3 are what?
(a) perpendicular(b) parallel(c) the same line(d) intersecting at one point
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.Find the gradient of the line through the points (1, 1) and (4, 7).
8.Write down the equation of a line with gradient -3 and y-intercept 4.
9.Find the midpoint of the points (0, 0) and (8, 6).
10.Find the distance between the points (1, 1) and (4, 5).
11.Write down the equation of the line through the origin with gradient 5.
12.State the gradient of the line y = 4x - 2.
13.A line passes through (2, 3) and has gradient 2. Write down its equation.
14.State the gradient of a line perpendicular to y = 2x + 3.
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.A ramp rises from (0, 0) to (5, 2). Find the gradient of the ramp.
16.A drone flies in a straight line from (1, 1) to (5, 4), where distances are in km. Find the distance it travels.
17.The midpoint of AB is (3, 5) and A is (1, 2). Find the coordinates of B.
18.A line with gradient 2 passes through the point (1, 3). Find its y-intercept.
19.A car's position in km from home is modelled by y = 60x + 20, where x is hours. How far from home is the car after 3 hours?
20.Show that the points (0, 0), (3, 4) and (6, 8) are collinear by comparing gradients.
Answer Key
1. a) 3
2. b) y = 2x + 5
3. a) 3
4. a) (4, 7)
5. c) 10
6. b) parallel
7. Refer to solution guide.
8. Refer to solution guide.
9. Refer to solution guide.
10. Refer to solution guide.
11. Refer to solution guide.
12. Refer to solution guide.
13. Refer to solution guide.
14. Refer to solution guide.
15. Refer to solution guide.
16. Refer to solution guide.
17. Refer to solution guide.
18. Refer to solution guide.
19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet
People Also Ask
What is the gradient of the line through (0, 0) and (2, 6)?
3, option (a) in this worksheet (Q1).
Which line has gradient 2 and y-intercept 5?
y = 2x + 5, option (b) in this worksheet (Q2).
What is the midpoint of (2, 3) and (6, 7)?
(4, 7), from the answer key on this page.
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