Question

A graph has the points (0, 6) and (9, 0). Find the y-intercept.

Answer 1

The y-intercept of a linear equation is the point where the line crosses the y-axis. This occurs when \( x = 0 \).

You already have one point on the line at the y-intercept, which is \( (0, 6) \). Therefore, the y-intercept is \( 6 \).

To confirm this using the two points you have, you can find the equation of the line that passes through the points \( (0, 6) \) and \( (9, 0) \).

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

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 6}{9 - 0} = \frac{-6}{9} = -\frac{2}{3}
\]

2. **Use the slope-intercept form of the line**:

The slope-intercept form is given by:

\[
y = mx + b
\]

where \( m \) is the slope and \( b \) is the y-intercept.

Using the slope \( m = -\frac{2}{3} \) and the point \( (0, 6) \), we can substitute \( (0, 6) \) into the equation:

\[
6 = -\frac{2}{3}(0) + b
\]

This simplifies to:

\[
6 = b
\]

Thus, the y-intercept \( b \) is indeed \( 6 \).

So, the y-intercept is:

\[
\boxed{6}
\]