Question

Find the slope and y-intercept that has infinite solutions to the equation

9
x
+
5
y
=
15
9x+5y=15

The slope would be
.

The y-intercept would be
. (Do not list as a coordinate point.)

Answer 1

To find the slope and y-intercept of the equation \( 9x + 5y = 15 \) that has infinite solutions, we first need to express it in slope-intercept form, which is \( y = mx + b \) where \( m \) is the slope and \( b \) is the y-intercept.

1. **Rearranging the equation**:

Start with the original equation:
\[
9x + 5y = 15
\]

Isolate \( y \):
\[
5y = 15 - 9x
\]
\[
5y = -9x + 15
\]
\[
y = -\frac{9}{5}x + 3
\]

2. **Identify slope and y-intercept**:

From the equation \( y = -\frac{9}{5}x + 3 \):
- The slope (\( m \)) is \( -\frac{9}{5} \).
- The y-intercept (\( b \)) is \( 3 \).

Since you asked for an equation with infinite solutions, any multiple of this equation (like \( 18x + 10y = 30 \), etc.) would have the same slope and y-intercept.

Thus, the answers are:
- The slope would be \( -\frac{9}{5} \).
- The y-intercept would be \( 3 \).