Question

witch equation represents a line with a slope of - 1/4 and a y intercept of 5/4

x + 4y = 5
x - 4y = 5
4x - y = -5
4x + y = -5

Answer 1

To find the equation of a line with a slope of \(-\frac{1}{4}\) and a y-intercept of \(\frac{5}{4}\), we can use the slope-intercept form of a linear equation, which is given by:

\[
y = mx + b
\]

where \(m\) is the slope and \(b\) is the y-intercept. Substituting the given values:

\[
y = -\frac{1}{4}x + \frac{5}{4}
\]

Now, let's manipulate this equation to compare it to the options given.

1. Start with the equation:
\[
y = -\frac{1}{4}x + \frac{5}{4}
\]

2. To eliminate the fraction, multiply the entire equation by 4:
\[
4y = -x + 5
\]
Rearranging gives:
\[
x + 4y = 5
\]

Now we can see that the correct answer corresponds to the first option listed:

**\(x + 4y = 5\)**.