Please answer with explanation and standard form

2x - 7y = -34.

Step-by-step explanation:

As the line we want is perpendicular to y= -7/2 x + 9 it's slope will be

-1 /(-7/2) = 2/7.

Now we find the point of intersection ofn the 2 given  lines:

x    + y = 10

3x - 4y = -12

Multiply the first equation by -3:

-3x - 3y = -30

Now add this last equation to the second one:

-7y =  -42

y = 6

Plug y = 6 into the first equation:

x + 6 = 10

x = 4.

So the point of intersection is (4, 6) and the equation we want passes through this, so using the point-slope form of  straight line we have:

y - 6 = 2/7(x - 4)

7y - 42 = 2(x - 4)

7y - 42 = 2x - 8

2x - 7y = -42 + 8

2x - 7y = -34

y=(2/7)x+(7/3)

Step-by-step explanation:

y=-7/2(x)+9

y=mx+c

Therefore, slope of line y is -7/2

Because line y perpendicular to the required line

Therefore, slope of the required line is 2/7

x+y=10 (1)

3x-4y = -12 (2)

(1) x 4:

4x+4y =40 (3)

(3) + (2)

4x+4y+3x-4y=28

x=4

by substituting x=4 into (1), we have

y=10-4=6

Therefore, the point that the line intersects is (4, 6)

let y=(2/7)x+c be the required equation

(4, 6):

6=(2/7)4+c

c=21/4

therefore, the required equation is y=(2/7)x+(7/3).