Calculate the equation of a line that is perpendicular to the line shown on the graph and that also shares the same y-intercept. (1 point) Responses y=12x−8 y equals Start Fraction 1 over 2 End Fraction x minus 8 y=2x−8 y equals 2 x minus 8 y=−2x+4 y equals negative 2 x plus 4 y=−12x+4 y equals negative Start Fraction 1 over 2 End Fraction x plus 4

Answer 1

To find a line that is perpendicular to the original line and shares the same y-intercept, we first need to determine the slope of the original line.

1. Identify the slope of the original line: If the equation of the given line is in the slope-intercept form \(y = mx + b\), then \(m\) is the slope. Without the exact equation provided, we cannot calculate the slope directly.
2. Find the slope of the perpendicular line: The slope of a line that is perpendicular to another line is the negative reciprocal of the original line's slope. If the original slope is \(m\), then the slope of the perpendicular line will be \(-\frac{1}{m}\).
3. Share the same y-intercept: The y-intercept \(b\) will remain the same as that of the original line.

Since the specific equation of the original line is not provided in your question, I will demonstrate how you would find the new line if you had the original Slop \(m\) and y-intercept \(b\):

• The equation of the perpendicular line can be formulated as: \[ y = -\frac{1}{m}x + b \]

Assuming an example:

Let's say the original line's equation was \(y = 2x - 8\) (where the slope \(m = 2\) and y-intercept \(b = -8\)):

1. The negative reciprocal of \(2\) is \(-\frac{1}{2}\).
2. The y-intercept is \(-8\).

The equation of the perpendicular line would then be: \[ y = -\frac{1}{2}x - 8 \]

Final Selection:

Based on the response options you provided:

• The equation must match the form \(y = -\frac{1}{2}x + b\) to reflect a slope of \(-\frac{1}{2}\) and if the y-intercept were \(4\), that would be incorrect for having the same y-intercept of the original line.

Let's confirm a match:

• If the slope is facing a match to one of your responses based on hypothetical slopes of the original line.

From your choices, I can identify candidates:

• y = -\frac{1}{2}x + 4 (incorrect, as it has a different y-intercept if that was the base intercept).

If you need a specific choice from your options and provided those intercept details, I'd rather instruct that based on available choices and the possible lack from the initial information.