Question

Find the slope and y intercept that has infinite solutions to the equation 4x+10y=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 \(4x + 10y = 25\) that has infinite solutions, we 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:
\[
4x + 10y = 25
\]

2. Solve for \(y\):
\[
10y = -4x + 25
\]
\[
y = -\frac{4}{10}x + \frac{25}{10}
\]
\[
y = -\frac{2}{5}x + 2.5
\]

From this equation, we can identify the slope and the y-intercept:
- The slope \(m = -\frac{2}{5}\).
- The y-intercept \(b = 2.5\).

However, for the equation to have infinite solutions, it must be equivalent to another equation of the same line. This means all coefficients have to maintain the same ratio.

Given that the equation is already in the necessary form, we conclude:

The slope would be **-\(\frac{2}{5}\)**.
The y-intercept would be **2.5**.