Question

Give that the slope of a line is
and a point on that line is (-1,3), what is the equation for that line in Point Slope Form?

Answer 1

the slope is 2/3

Answer 2

To write the equation of a line in point-slope form, we use the formula:

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

where \( m \) is the slope of the line, and \( (x_1, y_1) \) is a point on the line.

In your case, the point given is \((-1, 3)\). Thus, \( x_1 = -1 \) and \( y_1 = 3 \). You mentioned "the slope of a line is" but didn’t provide a specific value for the slope. Let's denote the slope as \( m \).

Substituting the values into the point-slope form:

\[ y - 3 = m(x - (-1)) \]

This simplifies to:

\[ y - 3 = m(x + 1) \]

So, the equation of the line in point-slope form is:

\[ y - 3 = m(x + 1) \]

If you provide a specific value for the slope \( m \), I can give you the exact equation.

Answer 3

Great! With a slope of \( m = \frac{2}{3} \) and the point \((-1, 3)\), we can substitute these values into the point-slope form equation.

The point-slope form is:

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

Substituting \( m = \frac{2}{3} \), \( x_1 = -1 \), and \( y_1 = 3 \):

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

This simplifies to:

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

So the equation of the line in point-slope form is:

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