Question

write an equation paraell to 5x+y=6 through the points (15,-4) leave answer in standard form

Answer 1

To find the equation of a line parallel to \(5x + y = 6\) that passes through the point \( (15, -4) \), we start by identifying the slope of the given equation.

1. **Find the slope of the original line:**
Rearranging \(5x + y = 6\) into slope-intercept form \(y = mx + b\):
\[
y = -5x + 6
\]
The slope \(m\) of this line is \(-5\).

2. **Use the same slope for the new line:**
Since parallel lines have the same slope, the slope of the desired line is also \(-5\).

3. **Use the point-slope form of the line equation:**
The point-slope form is given by:
\[
y - y_1 = m(x - x_1)
\]
where \( (x_1, y_1) = (15, -4) \) and \(m = -5\):
\[
y - (-4) = -5(x - 15)
\]
Simplifying this:
\[
y + 4 = -5x + 75
\]
\[
y = -5x + 71
\]

4. **Convert to standard form:**
To convert \(y = -5x + 71\) to standard form \(Ax + By = C\), we rearrange it:
\[
5x + y = 71
\]

The final answer, in standard form, is:
\[
\boxed{5x + y = 71}
\]