We are asked to write the equation of a line in standard form, given the slope of $\frac{1}{4}$ and the y-intercept of $-2$.

Step 1: Recall the slope-intercept form

The slope-intercept form of a line is given by: $y = mx + b$ Where $m$ is the slope and $b$ is the y-intercept.

For this problem:

• The slope $m = \frac{1}{4}$
• The y-intercept $b = -2$

So, the equation in slope-intercept form is: $y = \frac{1}{4}x - 2$

Step 2: Convert to standard form

The standard form of a line is written as: $Ax + By = C$ Where $A$, $B$, and $C$ are integers.

To convert $y = \frac{1}{4}x - 2$ into standard form:

1. Multiply the entire equation by 4 to eliminate the fraction: $4y = x - 8$
2. Rearrange the terms so that the $x$-term is on the left side: $x - 4y = 8$

This is the equation of the line in standard form: $x - 4y = 8$.

Final Answer:

$x - 4y = 8$

Let me know if you'd like further details or have any questions!

Here are 5 related questions for practice:

1. What is the slope of the line $2x - 3y = 6$?
2. How do you convert a line equation from standard form to slope-intercept form?
3. Write the equation of a line with slope $-3$ and y-intercept $5$.
4. What is the equation of a line perpendicular to $y = \frac{1}{4}x - 2$?
5. Find the x-intercept and y-intercept of the line $2x + 5y = 10$.

Tip: Always ensure the coefficients in standard form are integers, and it's common to write the equation with a positive $x$-coefficient.