Final answer:
The equation of the line perpendicular to x + 7y = 1 and passing through the point (0, -3) is 7x - y = 3.
Therefore, the correct answer is a.
Step-by-step explanation:
To understand why this is the correct answer, let's go through the steps again:
1. Determine the slope of the given line: The equation x + 7y = 1 is in standard form (Ax + By = C), where A = 1, B = 7, and C = 1.
To find the slope of this line, we can rearrange the equation in slope-intercept form (y = mx + b), where m represents the slope.
Solving for y, we have:
- - x + 7y = 1
- - 7y = -x + 1
- - y = (-1/7)x + 1/7
The slope of this line is -1/7.
2. Determine the slope of the perpendicular line: The slopes of perpendicular lines are negative reciprocals of each other. So, the slope of the perpendicular line will be the negative reciprocal of -1/7, which is 7.
3. Use the point-slope form: We have the slope (m = 7) and the point (0, -3).
Using the point-slope form of a line (y - y₁= m(x - x₁)), we can substitute the values to find the equation:
- - y - (-3) = 7(x - 0)
- - y + 3 = 7x
4. Simplify into standard form: To rewrite the equation in standard form (Ax + By = C), we move all terms to one side:
Therefore, the correct equation of the line perpendicular to x + 7y = 1 and passing through the point (0, -3) is 7x - y = 3.
The answer is option ⇒a. 7x - y = 3