JHS2 Mathematics · Term 2, Week 5
Patterns and Relations
Full lesson notes coming
Notes for this lesson are being prepared. The curriculum details below are complete and ready to use for your planning.
Curriculum details
- Strand
- Algebra (Strand 2)
- Sub-strand
- Patterns and Relations (2.1)
- Content standard
- B8.2.1.1 - Demonstrate the ability to draw table of values for a linear relation, graph the relation in a number plane, determine the gradient of the line and use it to write equation of a line of the form y = mx + c.
- Indicator
- B8.2.1.1.1 - Calculate the gradient of a line and use it to write equation of a line of the form y = mx + c.
- Suggested placement
-
Term 2, Week 5
(Week 17 of the year)
Our suggestion, laid out in curriculum order across three terms of twelve weeks. NaCCA does not fix the week, so follow your school's scheme of learning.
- Curriculum reference
-
Mathematics, Common Core Programme (JHS1-JHS3), 2023, p. 112
Transcribed from the official NaCCA publication. Check this page against the source.
Exemplars (from the NaCCA curriculum)
E.g.1 Explain the concept of gradient using real life examples and to discover the practical meaning of gradient.
The gradient is the measure of how steep the hill the rider is climbing is. The gradient is the slope (or steepness) of the roofing of the building. E.g.2 Determine the formula for calculating the gradient of a line.
The formula for calculating the gradient of a straight line is given as: ∆y = y 2 -y 1 ∆x x 2 -x 1 E.g.3 Determine the gradient when given two coordinates. Find the gradient of a line which passes through the point; i. A(1,1) and B(7,2) ii. P(-2,4) and Q(3,5) iii. C(3,-2) and D(-3,4) E.g.4 Determine the gradient of a straight line when its equation is given. Find the gradient from the equation of the straight line below
i. y = 5x + 13 ii. 2x - 8y + 3 = 0 iii. y = -3x + 12 E.g.5 Determine the gradient from a graph.
Determine the gradient of the line in the graph. From the graph, the coordinates are A (-8,-2), B (2,3). m = -2-3 = -5 = 1 -8-2 -10 2 The gradient of the line is 1 2 E.g.6 Determine the slope-intercept form of the equation of a straight line Hint: The equation of a straight line in slope-intercept form is y = mx + c i. Find the equation of a line with slope 2 and y-intercept -3. Hence find the value of y when x is 4. ii. Find the equation of a line in slope-intercept form having y-intercept 7 and 2 slope - 5 . 2 iii. Find the equation of a line with slope 1 and y-intercept 4. 2 E.g.7 Determine the point-slope form of the equation of a straight line Hint: The point-slope form of the equation of a straight line is y - y = m(x - x ) 1 1 i. Find the equation of a line with slope 2 that passes through the point (3, -1). 3 ii. Find the equation of a line that passes through the point (3, -7) and has the slope m = 5 . 4 iii. Find the equation of a line which passes through the points (5, 4) and (-10,- 2). iv. Write the equation 5x + 4y - 3 = 0 in the formy = mx + c. Hence state the gradient and the intercept.