Calculate the equation of a line that is perpendicular to the line shown on the graph and that also shares the same y-intercept.

Answer 1

To find the equation of a line that is perpendicular to another line and shares the same y-intercept, you would follow these steps:

1. Identify the original line's equation: If the original line is given in slope-intercept form (y = mx + b) where m is the slope and b is the y-intercept.

2. Determine the slope of the perpendicular line: If the slope of the original line is m, the slope of the line that is perpendicular to it will be -1/m. This is because the slopes of two perpendicular lines are negative reciprocals of each other.

3. Use the same y-intercept: The y-intercept remains the same as that of the original line.

4. Write the equation: Substitute the slope of the perpendicular line and the y-intercept into the slope-intercept form (y = mx + b).

Example:

Let's say the original line's equation is \(y = 2x + 3\).

• The slope (m) is 2, and the y-intercept (b) is 3.
• The slope of the perpendicular line would be \(-1/2\).
• Since it shares the same y-intercept, we have \(b = 3\).

The equation of the perpendicular line would be:

\[ y = -\frac{1}{2}x + 3 \]

If you have specific values for the original line, please provide them and I can calculate the perpendicular line's equation directly!