Question

find the gradients of line A and B

Answer 1

Step-by-step explanation:

refer to attachment

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Answer 2

The gradient of the line A and line B are 2 and - 1 respectively

Given :

The graph of the line A and B

To find :

The gradients of line A and B

Concept :

For the given two points $\sf{A( x_1 , y_1) \: \: and \: \: B( x_2 , y_2)}$

The gradient of the line AB is

$\displaystyle \sf{ = \frac{y_2 - y_1}{x_2 - x_1} }$

Solution :

Step 1 of 4 :

Find two points on the line A

From graph we see that two points on the line A are (0,1) & (2,5)

Step 2 of 4 :

Find gradient of line A

The gradient of line A

$\displaystyle \sf{ = \frac{5 - 1}{2 - 0} }$

$\displaystyle \sf{ = \frac{4}{2 } }$

$\displaystyle \sf{ =2 }$

Step 3 of 4 :

Find two points on the line B

From graph we see that two points on the line B are (5,0) & (0,5)

Step 4 of 4 :

Find gradient of line B

The gradient of line B

$\displaystyle \sf{ = \frac{5 - 0}{0 - 5} }$

$\displaystyle \sf{ = \frac{5 }{ - 5} }$

$\displaystyle \sf{ = - 1 }$

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