Answer :
To determine which of the given options is the correct equation of a line in slope-intercept form with a slope of [tex]\(\frac{1}{4}\)[/tex] and a [tex]\(y\)[/tex]-intercept at (0, -1), we'll follow these steps:
1. Identify the components of the slope-intercept form:
The general equation of a line in slope-intercept form is given by:
[tex]\[ y = mx + b \][/tex]
where [tex]\(m\)[/tex] is the slope and [tex]\(b\)[/tex] is the [tex]\(y\)[/tex]-intercept.
2. Substitute the given slope and [tex]\(y\)[/tex]-intercept into the equation:
We are given:
[tex]\[ m = \frac{1}{4} \][/tex]
and
[tex]\[ b = -1 \][/tex]
Substituting these values into the slope-intercept form equation, we get:
[tex]\[ y = \frac{1}{4}x - 1 \][/tex]
3. Compare with the given options:
[tex]\[ \begin{aligned} \text{A. } & y = \frac{1}{4} x - 1 \\ \text{B. } & y = 4 x - 1 \\ \text{C. } & y = \frac{1}{4} x + 1 \\ \text{D. } & y = -\frac{1}{4} x - \frac{1}{4} \end{aligned} \][/tex]
We see that option A matches exactly with our derived equation.
Therefore, the correct choice is
[tex]\[ \boxed{A. \ y = \frac{1}{4} x - 1} \][/tex]
1. Identify the components of the slope-intercept form:
The general equation of a line in slope-intercept form is given by:
[tex]\[ y = mx + b \][/tex]
where [tex]\(m\)[/tex] is the slope and [tex]\(b\)[/tex] is the [tex]\(y\)[/tex]-intercept.
2. Substitute the given slope and [tex]\(y\)[/tex]-intercept into the equation:
We are given:
[tex]\[ m = \frac{1}{4} \][/tex]
and
[tex]\[ b = -1 \][/tex]
Substituting these values into the slope-intercept form equation, we get:
[tex]\[ y = \frac{1}{4}x - 1 \][/tex]
3. Compare with the given options:
[tex]\[ \begin{aligned} \text{A. } & y = \frac{1}{4} x - 1 \\ \text{B. } & y = 4 x - 1 \\ \text{C. } & y = \frac{1}{4} x + 1 \\ \text{D. } & y = -\frac{1}{4} x - \frac{1}{4} \end{aligned} \][/tex]
We see that option A matches exactly with our derived equation.
Therefore, the correct choice is
[tex]\[ \boxed{A. \ y = \frac{1}{4} x - 1} \][/tex]
