Answer:
the equation of the line that passes through the point (-4,1) and is parallel to the line x - y = 6 is y = x + 5.
Explanation:
To find the equation of a line parallel to another line, we need to use the fact that parallel lines have the same slope. Here's how we can find the equation:
1. Given Information: The line passes through the point (-4,1) and is parallel to the line x - y = 6.
2. Original Line: The original line has the equation x - y = 6. To rewrite it in slope-intercept form (y = mx + b), we need to isolate y:
x - y = 6
-y = -x + 6
y = x - 6
3. Slope: The slope of the original line is 1, as seen in the equation y = x - 6. Parallel lines have the same slope, so the line we want to find will also have a slope of 1.
4. Equation: We can use the point-slope form of a linear equation to find the equation of the line passing through the point (-4,1) with a slope of 1:
y - y1 = m(x - x1)
Substituting the values, we have:
y - 1 = 1(x - (-4))
y - 1 = x + 4
y = x + 5