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. The line has two points on it and it goes through both. The points' coordinates are, (0, 4) and (-8, 0) (1 point) Responses 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 y=2x−8 y equals 2 x minus 8 y=12x−8

Answer 1

To find the equation of a line that is perpendicular to another line and shares the same y-intercept, we first need to find the slope of the line that passes through the given points \((0, 4)\) and \((-8, 0)\).

1. **Calculate the slope (m)** of the line through the points:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 4}{-8 - 0} = \frac{-4}{-8} = \frac{1}{2}
\]

2. **Determine the slope of the perpendicular line**:
The slope of a line that is perpendicular to another line is the negative reciprocal of the original slope. Thus,
\[
m_{\text{perpendicular}} = -\frac{1}{m} = -\frac{1}{\frac{1}{2}} = -2
\]

3. **Equation of the perpendicular line**:
Since the new line shares the same y-intercept as the line through the points, and the y-intercept from the point \((0, 4)\) is \(4\), we can write the equation in slope-intercept form \(y = mx + b\) using the slope we found and the y-intercept:
\[
y = -2x + 4
\]

Therefore, the equation of the line that is perpendicular to the original line and shares the same y-intercept is:

\[
\boxed{y = -2x + 4}
\]