This mathematics lesson covers using coordinate geometry to solve problems involving gradients, y-intercepts, and linear equations. It uses the example of a skateboard ramp to demonstrate how to: 1) Draw the side of a ramp on a number plane with a given vertical height and horizontal length. 2) Calculate the gradient and y-intercept of the original ramp. 3) Draw and find the gradient of a new, steeper ramp on the same number plane. 4) Write the equations for both the original and new ramp.

1. Mathematics Grade 8
Lesson 8
JASMIN C. ALANG-MIPARANUM

2. Q1. What is the gradient and y-intercept of 𝑦 =
7𝑥 − 5 ?
Q2. What is the gradient of the line joining
(3,5) and (-1, 9)?
Q3. Rewrite 2𝑥 + 3𝑦 − 6 = 0 in the form 𝑦 = 𝑚x
+ 𝑏
Q4. Draw a number plane and draw the

3. 3
Answer

4. The lesson is about: Using
your knowledge of Co-Ordinate
Geometry to solve real life
problems

5. Gradient – is the slope or steepness of a
line when viewing from left to right.
y-intercept – where a line cuts the
y- axis, where x=0.
x-intercept – where a line cuts the x-axis,
where y=0.

6. Joshua is a champion skateboard rider. He is
designing a ramp for himself to skate down
to complete a new trick. He uses a number
plane and a linear equation to design the
ramp. The vertical height of the ramp is 8
meters and the horizontal length of the ramp
is 20 meters.

7. Q1. Draw a diagram to show the side of
the ramp on a number plane. Place the
right angle of the ramp at the origin on
the number plane.
Q2. What is the y-intercept?
Q3. What is the x-intercept?
Q4. What is the gradient of the ramp?
Q5. Write an equation for the ramp.

8. 8

9. Joshua decided that the ramp was not steep
enough. He made the ramp 4 meters higher.
Q1. On the same diagram as above, draw a
diagram to show the new side of the ramp on the
number plane.
Q2. What is the gradient of the new ramp?
Q3. What is the new equation of the ramp?
Q4. If Joshua wanted the new ramp to have the
same gradient as the old ramp, what would the
new horizontal length have to be?

11. 11
o What were the key mathematical concepts addressed
in this lesson? o Your level of understanding of the
material in this lesson is high, moderate, or low?
o Has the lesson helped you to gain further insight into
aspects of the material covered?
o Describe any issue to your progress and achievement
in relation to the topic area?
o What would best assist your progress and
achievement in this topic area?

12. thank you …