Question

15. Find the equation of the line that is parallel to 2x + 5y - 7 = 0 and passes through the
mid-point of the line segment joining the points (2,7) and (-4,1).
16. Find the equation of the line that is perpendicular to 3x + 2y - 8 =0 and passes through
the mid-point of the line segment joining the points (5,-2) and (2, 2).
Find the equation of a straight line passing through the intersection of 2x + 5y - 4 = 0
parallel to the line 3x
7u​

Answer 1

Step-by-step explanation:

Given line: 2x+5y−7=0

5y=−2x+7

y=(5−2)x+57

So, the slope is 5−2

Hence, the slope of the line that is parallel to the given line will be the same, m=5−2

Now, the mid - point of the line segment joining point (2,7) and (−4,1) is 

(2(2−4),2(7+1))=(−1,4)

Thus, the equation of the line will be

y−y1=m(x−x1)

y−4=(5−2)(x+1)

5y−20=−2x−2

2x+5y=18

Answer 2

Answer:

Step-by-step explanation:

Given line: 2x+5y-7-0

5y=-2x+7

y=(5-2)x+57

So, the slope is 5-2

Hence, the slope of the line that is parallel to the

given line will be the same, m-5-2

Now, the mid-point of the line segment joining

point (2,7) and (-4,1) is

(2(2-4),2(7+1))=(-1,4)

Thus, the equation of the line will be

y-y1-m(x-x1)

y-4-(5-2)(x+1)

5y-20--2x-2

2x+5y=18