Question

Which equation is a point slope form equation for line AB
?

Responses

y+1=23(x−4)
y plus 1 equals 2 over 3 left parenthesis x minus 4 right parenthesis

y+1=−32(x−4)
y plus 1 equals negative 3 over 2 left parenthesis x minus 4 right parenthesis

y+1=−23(x−4)
y plus 1 equals negative 2 over 3 left parenthesis x minus 4 right parenthesis

y+1=32(x−4)
y plus 1 equals 3 over 2 left parenthesis x minus 4 right parenthesis
A graph with a line running through point A, with coordinates (4, -1), and point B, with coordinates (-2, 3)

Answer 1

To find the correct point-slope form of the equation for line AB, we need to determine the slope of the line that passes through the points \( A(4, -1) \) and \( B(-2, 3) \).

1. **Calculate the slope (m)** using the formula:

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

Here, \( (x_1, y_1) = (4, -1) \) and \( (x_2, y_2) = (-2, 3) \).

\[
m = \frac{3 - (-1)}{-2 - 4} = \frac{3 + 1}{-6} = \frac{4}{-6} = -\frac{2}{3}
\]

2. **Use point-slope form**: The point-slope form of a line is given by:

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

Here, we can use point \( A(4, -1) \), where \( x_1 = 4 \) and \( y_1 = -1 \), and substitute the slope \( m = -\frac{2}{3} \):

\[
y - (-1) = -\frac{2}{3}(x - 4)
\]

This simplifies to:

\[
y + 1 = -\frac{2}{3}(x - 4)
\]

3. Compare this with the options provided. The corresponding point-slope form equation is:

\[
y + 1 = -\frac{2}{3}(x - 4)
\]

So, the correct equation in point-slope form for line AB is:

**y + 1 = -\frac{2}{3}(x - 4)** (which is the third response).