13

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

7
𝑥
+
2
𝑦
=
25
7x+2y=25

The slope would be
.

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

1 answer

To find the slope and y-intercept of the equation \( 7x + 2y = 25 \) that has infinite solutions, we need to express the equation in the slope-intercept form, \( y = mx + b \), where \( m \) represents the slope and \( b \) represents the y-intercept.

  1. Start with the original equation: \[ 7x + 2y = 25 \]

  2. Isolate \( y \): \[ 2y = -7x + 25 \]

  3. Divide everything by 2 to solve for \( y \): \[ y = -\frac{7}{2}x + \frac{25}{2} \]

From the equation \( y = -\frac{7}{2}x + \frac{25}{2} \):

  • The slope (\( m \)) is \( -\frac{7}{2} \).
  • The y-intercept (\( b \)) is \( \frac{25}{2} \).

Thus, the final answer is:

The slope would be \( -\frac{7}{2} \).

The y-intercept would be \( \frac{25}{2} \).