Question

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.)

Answer 1

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 \( \frac{25}{2} \).