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Write the equation of a line that is PERPENDICULAR to x + 7y = 1 and goes through the point (0, -3).

a. 7x - y = 3
b. 7x - y = -3
c. -7x + y = 3
d. -7x + y = -3

1 Answer

4 votes

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:

  • - 7x - y - 3 = 0

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

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