Question

Find slope of the line passing through 3y & -1x write the equation

Answer 1

To find the slope of the line that passes through the points represented by \(3y\) and \(-1x\), we need to determine what points these correspond to.

Assuming \(3y\) represents the point \((x_1, y_1) = (0, 3)\) and \(-1x\) represents the point \((x_2, y_2) = (-1, 0)\).

However, if the intent was to have \(x = -1\) and \(y = 3\), we can rewrite the points as follows:

1. Point 1: \( (0, 3) \)
2. Point 2: \( (-1, 0) \)

Now to find the slope \(m\) of the line that passes through these two points, we use the slope formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substituting \( (x_1, y_1) = (0, 3) \) and \( (x_2, y_2) = (-1, 0) \):

\[
m = \frac{0 - 3}{-1 - 0} = \frac{-3}{-1} = 3
\]

So, the slope of the line is \(3\).

Next, to write the equation of the line, we can use the point-slope form of a line, which is:

\[
y - y_1 = m(x - x_1)
\]

Using point \((0, 3)\) and the slope \(3\):

\[
y - 3 = 3(x - 0)
\]

Simplifying this gives:

\[
y - 3 = 3x
\]
\[
y = 3x + 3
\]

Thus, the equation of the line passing through those points is:

\[
y = 3x + 3
\]