Question

How to find the gradient of the straight lines? I don’t want direct answer, I want explanation please. I’m confused how can I find the x and y axis

Answer 1

Answer:

Question 27

$\textsf{(a)} \quad -\dfrac{6}{5}$

$\textsf{(b)} \quad \dfrac{1}{10}$

$\textsf{(c)} \quad \dfrac{4}{5}$

Question 28

$\textsf{(a)} \quad \dfrac{6}{0}=\textsf{und\:\!efined}$

$\textsf{(b)} \quad -\dfrac{3}{10}$

$\textsf{(c)} \quad \dfrac{3}{10}$

Step-by-step explanation:

The gradient of a straight line can be found by dividing the difference in the y-coordinates by the difference in the x-coordinates between two points on the line.

A positive gradient slopes up from left to right.

A negative gradient slopes down from left to right.

$\boxed{\begin{minipage}{4.3cm}\underline{Gradient Formula}\\\\ m=\dfrac{y_2-y_1}{x_2-x_1} \\\\where (x_1,y_1) and (x_2,y_2) \\are two points on the line.\end{minipage}}$

We can use the formula to find the gradients, or we can simply calculate the change in y and change in x by looking at the graph.

Example:

If we take line (a) from question 27 as an example.

• The change in y from the beginning to the end of the line is 6 units.
• The change in x from the beginning to the end of the line is 5 units.
• The line slopes down, so the gradient is negative.

Therefore, the gradient is -6/5.

Using the gradient formula, define two points on the line:

• Let (x₁, y₁) = (0, 6)
• Let (x₂, y₂) = (5, 0)

Input the points into the formula:

$\textsf{Gradient}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{0-6}{5-0}=-\dfrac{6}{5}$

Solutions

Question 27

(a)  The gradient is -6/5, as calculated above.

(b)  The change in y is 1 unit and the change in x is 10 units. The line slopes up so the gradient is positive.  Therefore, the gradient is 1/10.

(c)  The change in y is 4 units and the change in x is 5 units. The line slopes up so the gradient is positive.  Therefore, the gradient is 4/5.

Question 28

(a)  The change in y is 6 units and the change in x is 0 units. Therefore, the gradient is undefined since anything divided by 0 is undefined.

(b)  The change in y is 3 units and the change in x is 10 units. The line slopes down so the gradient is negative.  Therefore, the gradient is -3/10.

(c)  The change in y is 3 units and the change in x is 10 units. The line slopes up so the gradient is positive.  Therefore, the gradient is 3/10.