Question

write an equation paraell to 5x+y=6 through the points (6,1) leave answer in standard form

Answer 1

To find the equation of a line parallel to \(5x + y = 6\), we first need to determine the slope of the given line. The equation is in the standard form \(Ax + By = C\).

1. Rearranging to slope-intercept form \(y = mx + b\):
\[
y = -5x + 6
\]
From this, we can see that the slope \(m\) is \(-5\).

Since parallel lines share the same slope, the slope of the new line will also be \(-5\). Now we use the point-slope form of the equation of the line, which is given by:
\[
y - y_1 = m(x - x_1)
\]
Where \((x_1, y_1)\) is the point through which the line passes (in this case, \((6, 1)\)), and \(m\) is the slope.

2. Substituting \(m = -5\), \(x_1 = 6\), and \(y_1 = 1\):
\[
y - 1 = -5(x - 6)
\]

3. Distributing the \(-5\):
\[
y - 1 = -5x + 30
\]

4. Adding \(1\) to both sides:
\[
y = -5x + 31
\]

5. To convert this to standard form \(Ax + By = C\), we can rearrange it:
\[
5x + y = 31
\]

Thus, the equation of the line parallel to \(5x + y = 6\) that passes through the point \((6, 1)\) is:

\[
\boxed{5x + y = 31}
\]