Answer:
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 on the vertical axis) / (change in the value of x on the horizontal axis)
The equation of the given line is
9x+7y=4
7y = 4 - 9x = -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 that 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
c = - 85/9
The equation becomes
y = 7x/9 - 85/9
