13

Question

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

6
x
+
2
y
=
25
6x+2y=25

The slope would be
.

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

Answer 1

For an equation to have infinite solutions, it must represent the same line. The given equation is

\[ 6x + 2y = 25. \]

First, let's rearrange the equation into the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

1. Start with the original equation:

   \[ 6x + 2y = 25. \]

2. Subtract \( 6x \) from both sides:

   \[ 2y = -6x + 25. \]

3. Now, divide every term by 2:

   \[ y = -3x + \frac{25}{2}. \]

From this, we can identify:

• Slope (m): The coefficient of \( x \) is \(-3\).
• Y-intercept (b): The constant term is \(\frac{25}{2}\).

Thus, the slope would be -3 and the y-intercept would be \(\frac{25}{2}\).

To summarize:

• The slope would be: -3.
• The y-intercept would be: \(\frac{25}{2}\).