Put the following equation of a line into slope-intercept form, simplifying all fractions: 20x + 4y = 8

Understand the Problem

The question is asking to convert the given equation of a line, which is in standard form, into slope-intercept form. The slope-intercept form is expressed as y = mx + b, where m is the slope and b is the y-intercept. The task also requires simplifying any fractions that may arise during the conversion.

Answer

The equation in slope-intercept form is $y = -5x + 2$.

Steps to Solve

Isolate the variable y

Start with the original equation:

$$ 20x + 4y = 8 $$

To isolate $y$, subtract $20x$ from both sides:

$$ 4y = 8 - 20x $$

Divide by the coefficient of y

Next, divide every term by 4 to solve for $y$:

$$ y = \frac{8}{4} - \frac{20x}{4} $$

Simplify the fractions

Simplifying the fractions gives:

$$ y = 2 - 5x $$

Rearrange into slope-intercept form

Now, rearrange the equation to place it in the standard slope-intercept form $y = mx + b$:

$$ y = -5x + 2 $$

The slope-intercept form of the equation is

$$ y = -5x + 2 $$

More Information

In the slope-intercept form, the coefficient of $x$, which is $-5$, represents the slope of the line, indicating it decreases as $x$ increases. The constant term $2$ represents the y-intercept, meaning the line crosses the y-axis at $(0, 2)$.

Tips

Forgetting to distribute a negative sign when moving terms around.
Not simplifying fractions fully.
Misidentifying the slope and y-intercept after conversion.

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