Answer:
Explanation:
To find an equation for the line perpendicular to the line 4x - 5y = 1 and having the same y-intercept as 7x + 9y = 9, you can follow these steps:
Step 1: Find the slope of the given line 4x - 5y = 1.
To do this, rearrange the equation into slope-intercept form (y = mx + b), where m represents the slope:
4x - 5y = 1
-5y = -4x + 1
y = (4/5)x - 1/5
The slope of the line is 4/5.
Step 2: Determine the slope of the line perpendicular to the given line.
Since the two lines are perpendicular, the slope of the perpendicular line is the negative reciprocal of the slope of the given line. In this case, the slope of the perpendicular line is -5/4.
Step 3: Use the given y-intercept to form the equation of the perpendicular line.
The given line 7x + 9y = 9 has a y-intercept of 1. This means that the point (0, 1) lies on the line.
Using the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, we can write the equation of the perpendicular line as:
y = (-5/4)x + 1
Therefore, the equation for the line perpendicular to 4x - 5y = 1 and having the same y-intercept as 7x + 9y = 9 is y = (-5/4)x + 1.