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

Question 27

`\textsf{(a)} \quad -(6)/(5)`

`\textsf{(b)} \quad (1)/(10)`

`\textsf{(c)} \quad (4)/(5)`

Question 28

`\textsf{(a)} \quad (6)/(0)=\textsf{und\:\!efined}=\textsf{no gradient}`

`\textsf{(b)} \quad -(3)/(10)`

`\textsf{(c)} \quad (3)/(10)`

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=(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}=(y_2-y_1)/(x_2-x_1)=(0-6)/(5-0)=-(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. Therefore, this line has no gradient.

(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.

Attachment

I have marked the change in y (green) and the change in x (blue) for line (c) on both graphs.