Question

Find the slope and y-intercept that has infinite solutions to the equation Click Here for Help Video

8
𝑥
+
2
𝑦
=
25
8x+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 \(8x + 2y = 25\) that has infinite solutions, we first need to express the equation in slope-intercept form, which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

1. Start with the original equation:
\[
8x + 2y = 25
\]

2. Isolate \(y\) on one side. First, subtract \(8x\) from both sides:
\[
2y = -8x + 25
\]

3. Now divide every term by \(2\) to solve for \(y\):
\[
y = -4x + 12.5
\]

From this form, we can identify the slope and the y-intercept:

- The slope (\(m\)) is \(-4\).
- The y-intercept (\(b\)) is \(12.5\).

Thus:

- The slope would be \(-4\).
- The y-intercept would be \(12.5\).