Question

Write an equation for the line passing through the points (5,-3), (5, 7).

Option A: y=−3x+5
Option B: y=7x−30
Option C: x=5
Option D: y=2x−13

Answer 1

The correct answer is option A: y=−3x+5. To write the equation of a line passing through two points, we need to find the slope and the y-intercept. Option A is the correct answer because it represents a vertical line passing through the point (5, -3).

Step-by-step explanation:

The correct answer is option A: y=−3x+5.

To write the equation of a line passing through two points, we need to find the slope and the y-intercept.

The slope (m) can be found using the formula m = (y2 - y1) / (x2 - x1). In this case, the two points are (5, -3) and (5, 7). Since the x-coordinates are the same, the denominator is zero and the slope is undefined.

Since the slope is undefined, we cannot write the equation of the line in the form y = mx + b. Therefore, options B, C, and D are incorrect.

To find the equation of a line passing through two points, you need to calculate the slope (m) and then use one of the points to find the y-intercept (b) if the line is not vertical. In this case, both points have the same x-coordinate (5), which indicates a vertical line. For a vertical line, the equation does not have a y-intercept, and is simply x equal to the shared x-coordinate of the points.

Option A is the correct answer because it represents a vertical line passing through the point (5, -3).