Write an equation of the line containing the given point and perpendicular to the given line:
(7,- 4); 9x+7y=4

Step-by-step explanation:

The equation of a straight line can be represented in the slope intercept form as

y = mx + c

Where

m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)

The equation of the given line is

9x+7y=4

7y = - 9x + 4

y = -9x/7 + 4/7

Comparing with the slope intercept form, slope = - 9/7

If the line passing through the given point is perpendicular to the given line, it means its slope is the negative reciprocal of the slope of the given line.

Therefore, the slope of the line passing through (7,-4) is 7/9

To determine the intercept, we would substitute m = 7/9, x = 7 and y = -4 into y = mx + c. It becomes

- 4 = 7/9×7 + c = 49/9 + c

c = - 4 - 49/9 = -85/9

The equation becomes

y = 7x/9 - 85/9

Step-by-step explanation:

any eq. of line perpendicular to 9x+7y=4 is

7x-9y=a

it passes  through (7,-4)

7(7)-9(-4)=a

49+36=a

a=85

reqd. eq. is 7x-9y=85