# Mathematics Worksheet/Equations of Straight Line

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1. Determine the gradient of a segment in line that connecting points:
1. ${\displaystyle \!X=(\!4,\!2)}$ and ${\displaystyle \!Y=(\!-3,\!-4)}$
2. ${\displaystyle \!A=(\!-5,\!-2)}$ and ${\displaystyle \!B=(\!3,\!4)}$
3. ${\displaystyle \alpha =(\!5,\!-3)}$ and ${\displaystyle \beta =(\!-2,\!8)}$
4. ${\displaystyle \lambda =(\!-6,\!3)}$ and ${\displaystyle \Delta =(\!4,\!1)}$
5. ${\displaystyle \!P=(\!-4,\!7)}$ and ${\displaystyle \!Q=(\!6,\!-3)}$
6. ${\displaystyle \!E=(\!7,\!5)}$ and ${\displaystyle \!F=(\!4,\!6)}$
7. ${\displaystyle \kappa =(\!-5,\!-2)}$ and ${\displaystyle \Omega =(\!-4,\!-9)}$
8. ${\displaystyle \!M=(\!-3,\!4)}$ and ${\displaystyle \!N=(\!5,\!-6)}$
9. ${\displaystyle \!R=(\!-5,\!1)}$ and ${\displaystyle \!S=(\!-4,\!-10)}$
10. ${\displaystyle \!C=(\!3,\!-5)}$ and ${\displaystyle \!D=(\!5,\!-3)}$
2. Find the gradient line from:
1. ${\displaystyle \!x+\!y=\!14}$
2. ${\displaystyle \!3x-\!5y=\!11}$
3. ${\displaystyle \!5x+\!4y=\!41}$
4. ${\displaystyle \!x-\!y=\!15}$
5. ${\displaystyle \!3(\!2x+\!5y)=\!3}$
6. ${\displaystyle \!5x-\!y=\!18}$
7. ${\displaystyle \!6x+\!3y=\!62}$
8. ${\displaystyle \!10x-\!5y=\!75}$
9. ${\displaystyle \!7x+\!3y=\!-8}$
10. ${\displaystyle \!3x-\!5y=\!-30}$
11. ${\displaystyle \!5x+\!9y=\!-2}$
12. ${\displaystyle \!4x+\!y=\!0}$
13. ${\displaystyle \!6x-\!3y=\!0}$
14. ${\displaystyle \!4(\!3x+\!y)=\!8}$
15. ${\displaystyle \!2x-\!0,5y=\!-7}$
16. ${\displaystyle \!1,5x+\!2,5y=\!21}$
17. ${\displaystyle \!2,4x+\!1,5y=\!14,7}$
18. ${\displaystyle \!3,2x-\!2,3y=\!5}$
19. ${\displaystyle \!4,5x+\!2,7y=\!18,9}$
20. ${\displaystyle \!6,7x-\!1,9y=\!19,2}$
3. Draw in the Cartesian diagram if known the four points are:
1. ${\displaystyle \!A=\!(\!4,\!-2),\!B=\!(\!3,\!3),\!C=\!(\!-6,\!3),\!D=\!(\!5,\!4)}$
2. ${\displaystyle \!A=\!(\!-7,\!-1),\!B=\!(\!4,\!-2),\!C=\!(\!-1,\!-9),\!D=\!(\!-4,\!3)}$
3. ${\displaystyle \!A=\!(\!-5,\!5),\!B=\!(\!6,\!-6),\!C=\!(\!-3,\!3),\!D=\!(\!2,\!-2)}$
4. ${\displaystyle \!A=\!(\!1,\!-10),\!B=\!(\!-3,\!-6),\!C=\!(\!4,\!7),\!D=\!(\!-6,\!1)}$
5. ${\displaystyle \!A=\!(\!-2,\!-2),\!B=\!(\!-5,\!7),\!C=\!(\!1,\!3),\!D=\!(\!-9,\!5)}$
4. From the questions number 3, calculate the gradient of line AB and line CD.
5. From the questions number 3, are the both lines parallel? If not, give the reason.