Question

If the equation of a line is y = 3x + 5, what would be the equation of the line perpendicular to the line that also shares the same y-intercept?
*
1 point
y = -1/3
x = 5
y = 3x - 5
y = -1/3x +5

Answer 1

In the standard (x, y) coordinate plane, what is the midpoint of the line segment with endpoints at (-5, 4) and (-3, 6)?
*
1 point
(4, -5)
(5, -4)
(-4, 5)
(-5, 4)
(-1, 8)

Answer 2

To find the equation of a line that is perpendicular to the line \( y = 3x + 5 \) and shares the same y-intercept, we need to first determine the slope of the perpendicular line.

The slope of the given line \( y = 3x + 5 \) is \( 3 \). The slope of a line that is perpendicular to another line is the negative reciprocal of the original slope. Therefore, the slope of the perpendicular line is:

\[
-\frac{1}{3}
\]

Since the perpendicular line needs to share the same y-intercept as the original line, which is \( 5 \) (from the equation \( y = 3x + 5 \)), we can write the equation of the perpendicular line using the slope-intercept form \( y = mx + b \):

\[
y = -\frac{1}{3}x + 5
\]

So the equation of the line perpendicular to \( y = 3x + 5 \) that also shares the same y-intercept is:

\[
y = -\frac{1}{3}x + 5
\]

Therefore, the correct answer is:

**y = -1/3x + 5**

Answer 3

To find the midpoint of a line segment with endpoints \((x_1, y_1)\) and \((x_2, y_2)\), we can use the midpoint formula:

\[
\text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]

Given the endpoints \((-5, 4)\) and \((-3, 6)\), we can substitute \(x_1 = -5\), \(y_1 = 4\), \(x_2 = -3\), and \(y_2 = 6\) into the formula:

1. Calculate the x-coordinate of the midpoint:

\[
x_{\text{mid}} = \frac{-5 + (-3)}{2} = \frac{-5 - 3}{2} = \frac{-8}{2} = -4
\]

2. Calculate the y-coordinate of the midpoint:

\[
y_{\text{mid}} = \frac{4 + 6}{2} = \frac{10}{2} = 5
\]

Thus, the midpoint is:

\[
(-4, 5)
\]

Therefore, the answer is:

**(-4, 5)**