00:01
Hi, in this question, given that the line is passing through the point (-4 ,5 ,3 ,2), first we have to find the slope m which is y2 -y1, 2 -y divided by x2 -x1 which is 3 plus 4 which is equal to minus 3 by 7.
00:22
Next we have to write the equation of line which is y -y1 equals m into x -x1.
00:31
On substituting the values in this, then we get y minus, consider this point, 2 equals m which is minus 3 by 7 into x -3 which implies y equals minus 3 by 7 x minus into minus plus 9 by 7 plus 2.
00:53
On further simplifying, then we get y equals minus 3 by 7 x plus 23 by 7.
01:04
Next we have to compare this with y equals mx plus c, then we can conclude that the slope m is minus 3 by 7.
01:17
Let the equation of the straight line passing through the point (-1 ,2), which is y equals m1x plus c.
01:32
On substituting here, then we get 2 equals m1 into minus 1 plus c.
01:38
So, 2 equals minus m1 plus c.
01:42
Here this line is parallel to the above line.
01:46
This is equation number 1 and this is equation number 2.
01:50
Here 1 is parallel to equation 2.
01:56
So, we can write it as m1 equals m2.
02:00
So, here m1 slope is also equal to minus 3 by 7.
02:06
On substituting here, then we can conclude that the equation of line is y equals minus 3 by 7 x plus, here we get c equals 11 by 7 which is the required answer.
02:29
Next in part b, given that the line is 4x plus 5y minus 5 equals 0.
02:40
From this, we have to write the slope intercept form.
02:43
So, 5y equals 5 minus 4x.
02:46
Y equals 5 by 5 minus 4 by 5 x.
02:51
Hence conclude that y equals 1 minus 4 by 5 x...