Question

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

Answer 1

The points (6, 0) and (9, 0) indicate that both of these points are on the x-axis, specifically where \( y = 0 \). The y-intercept of a graph is the point where the graph crosses the y-axis, which occurs when \( x = 0 \).

To find the y-intercept, we need to determine if the points (6, 0) and (9, 0) lie on a line, and if so, determine the equation of that line. The vertical position of the line (its y-value) will help us find the y-intercept.

Since both points have a y-value of 0, if we were to express the line passing through these points as a linear equation:

1. Identify the slope \( m \):

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

This indicates that the line is horizontal.

2. The equation of a horizontal line is given by \( y = b \), where \( b \) is the constant y-value. Given that the line passes through the points (6, 0) and (9, 0), we find:

\[
y = 0
\]

This means the line does not intersect the y-axis except at \( y = 0 \).

Thus, the y-intercept of the graph is:

\[
\boxed{0}
\]

The line itself doesn't cross the y-axis at any point other than the origin (0, 0).