Patterns and Relations · JHS2 Mathematics

Lesson notes

Learning Objectives

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.

By the end of the lesson, learners can:

Explain the concept of gradient as a measure of steepness using real-life examples such as hills, ramps, and roofing.
Calculate the gradient of a line given two coordinates using the formula m = (y2 - y1) / (x2 - x1).
Determine the gradient of a straight line from its equation in the form y = mx + c, and by rearranging equations into this form.
Read the gradient of a line directly from a graph by identifying two points on the line and applying the gradient formula.
Write the equation of a line in the form y = mx + c given the slope and y-intercept, and given the slope and a point on the line (point-slope form leads to slope-intercept form).

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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.

Wide colour table depicts a bicycle, a vehicle. The wide colour table is arranged with horizontal divisions,... — A wide colour table depicts a bicycle, a vehicle. The wide colour table is arranged with horizontal divisions, vertical divisions, coloured regions.

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.

Wide black-and-white mathematical teaching visual is organised as a table with horizontal divisions, vertical... — A wide black-and-white mathematical teaching visual is organised as a table with horizontal divisions, vertical divisions, open white space around the main marks. Visible labels, values, and notation include: line; Уı; УЗ-УІ; =х,-×→; X1; x2; The formula for calculating the gradient of a straight; sx=×-У; хz-×1.

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

Wide black-and-white mathematical teaching visual is organised as a worked calculation with vertical divisions, open... — A wide black-and-white mathematical teaching visual is organised as a worked calculation with vertical divisions, open white space around the main marks. Visible labels, values, and notation include: y=5x+ 13; ii. 2x-8y +3= 0; їїi. y = -3x + 12; yemxre; gradient y-axis intercept.

i. y = 5x + 13
ii. 2x - 8y + 3 = 0
iii. y = -3x + 12
E.g.5 Determine the gradient from a graph.

Line graph marks A at (-8, -2) and B at (2, 3), with changes in x and y labelled; the worked calculation gives a... — A line graph marks A at (-8, -2) and B at (2, 3), with changes in x and y labelled; the worked calculation gives a gradient of 1/2. The wide colour table is arranged with horizontal divisions, vertical divisions, coloured regions.

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.