Longman NSS Mathematics In Action 4a Solution

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How to Solve Longman NSS Mathematics in Action 4a Problems

If you are looking for a comprehensive guide on how to solve Longman NSS Mathematics in Action 4a problems, you have come to the right place. This article will show you step-by-step solutions to some of the most common and challenging questions in this textbook. You will also learn some useful tips and tricks on how to approach different types of problems and how to check your answers.

Longman NSS Mathematics in Action 4a is a textbook designed for students who are preparing for the Hong Kong Diploma of Secondary Education (HKDSE) Mathematics examination. It covers topics such as equations of straight lines, quadratic functions, inequalities, trigonometric functions, exponential and logarithmic functions, and more. The textbook provides clear explanations, examples, exercises, and activities to help students master the concepts and skills required for the exam.

Equations of Straight Lines

One of the topics covered in Longman NSS Mathematics in Action 4a is equations of straight lines. A straight line is a set of points that satisfy a linear equation of the form y = mx + c, where m is the slope and c is the y-intercept. The slope measures how steep the line is, and the y-intercept is the point where the line crosses the y-axis.

To find the equation of a straight line, you need to know either two points on the line or one point and the slope. If you know two points on the line, you can use the formula m = (y2 - y1) / (x2 - x1) to find the slope, and then substitute one point into y = mx + c to find the y-intercept. If you know one point and the slope, you can substitute them into y = mx + c to find the y-intercept directly.

For example, suppose you want to find the equation of a straight line that passes through the points (1, 2) and (3, 6). You can use the formula m = (y2 - y1) / (x2 - x1) to find the slope:

m = (6 - 2) / (3 - 1)

m = 4 / 2

m = 2

Then you can substitute one point into y = mx + c to find the y-intercept:

y = mx + c

2 = 2(1) + c

c = 0

Therefore, the equation of the straight line is y = 2x.

Example 1

Find the equation of a straight line that passes through the point (2, -3) and has a slope of -5.

Solution

We can substitute the point and the slope into y = mx + c to find the y-intercept:

y = mx + c

-3 = -5(2) + c

c = 7

Therefore, the equation of the straight line is y = -5x + 7.

Example 2

Find the equation of a straight line that passes through the points (-1, 4) and (3, -2).

Solution

We can use the formula m = (y2 - y1) / (x2 - x1) to find the slope:

m = (-2 - 4) / (3 - (-1))

m = -6 / 4

m = -3/2

Then we can substitute one point into y = mx + c to find the y-intercept:

y = mx + c

4 = (-3/2)(-1) + c

c = 5/2

Therefore, the equation of the straight line is y = (-3/2)x + (5/2). ec8f644aee