Answer:
So, the equation of the line parallel to \(y = x - 5\) and passing through the point \((3, 0)\) is \(y = x - 3\).
Step-by-step explanation:
The equation of a line can be expressed in the form \(y = mx + b\), where \(m\) is the slope of the line, and \(b\) is the y-intercept.
For a line parallel to \(y = x - 5\), it will have the same slope as this line because parallel lines have equal slopes. The given line \(y = x - 5\) has a slope of 1 (the coefficient of \(x\)).
Now, we can use the point-slope form of the equation of a line, 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.
Given the point \((3, 0)\) and the slope \(m = 1\), we can substitute these values into the point-slope form:
\[y - 0 = 1(x - 3)\]
Simplifying, we get:
\[y = x - 3\]
