4x Write an equation of the line that is parallel to 5x+20y=10 and passes through the point (8,3) A y=4x-29 B y=4x+35 C y=(1)/(4)x-1 D y=-(1)/(4)x+3 E y=-(1)/(4)x+5

## Step 1
The given equation of the line is $5x + 20y = 10$. We need to convert this equation into the slope-intercept form, which is $y = mx + b$, where $m$ is the slope of the line and $b$ is the y-intercept.

## Step 2
To convert the given equation into slope-intercept form, we divide the entire equation by 20. This gives us $y = -\frac{1}{4}x + \frac{1}{2}$.

## Step 3
The slope of the given line is $-\frac{1}{4}$. Since parallel lines have the same slope, the slope of the line we are looking for is also $-\frac{1}{4}$.

## Step 4
We are given a point (8,3) that lies on the line we are looking for. We can use the point-slope form of a line equation, which is $y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is a point on the line and $m$ is the slope.

## Step 5
Substituting the given point and slope into the point-slope form gives us $y - 3 = -\frac{1}{4}(x - 8)$.

## Step 6
Solving this equation for $y$ gives us the equation of the line in slope-intercept form: $y = -\frac{1}{4}x + 5$.