Question

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+4
y equals negative Start Fraction 1 over 2 End Fraction x plus 4

y=2x−8
y equals 2 x minus 8

y=−2x+4
y equals negative 2 x plus 4

y=12x−8

Answer 1

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

1. **Identify the slope of the original line**: The slopes of perpendicular lines are negative reciprocals of each other.

2. **Find the y-intercept**: The y-intercept is the value where the line crosses the y-axis (this is usually given in the form \( b \) in \( y = mx + b \)).

3. **Define the new line**: Using the y-intercept of the original line and the negative reciprocal of its slope, we can write the equation of the new line.

Since the problem did not provide the graph or the original line equation, I cannot directly compute this for you. However, I can guide you on how to approach it:

- If the original line has the equation \( y = mx + b \):
- The slope of the original line is \( m \).
- The slope of the new line (perpendicular) will be \( -\frac{1}{m} \).
- The y-intercept \( b \) stays the same for both lines.

Using these steps, substitute these values into the equation format \( y = -\frac{1}{m}x + b \) to find the perpendicular line equation which shares the same y-intercept.

If you provide the original line's equation or its slope, I can help calculate the specific perpendicular line's equation.