Final answer:
To write the equation of a line parallel to a given line, we use the same slope as the given line. The point-slope form of the line equation is applied using the point (6, –2) and the known slope. The final equation will be in the form y + 2 = m(x - 6), where m is the slope of the parallel line.
Step-by-step explanation:
To write an equation of a line that is parallel to another line and passes through a specific point, you must first know the slope of the given line. Since lines that are parallel have equal slopes, we can use the same slope for our new line. Let's assume the slope of the given line is m. If the point through which the new line passes is (6, –2), then we can use the point-slope form of a line equation:
y - y1 = m(x - x1)
where (x1, y1) is the point (6, –2). Plugging in the values, we get:
y + 2 = m(x - 6)
Once the slope m is known, it can be substituted into the equation above to provide the full equation of the line. If the slope of the given line is not provided, it can be determined using two points on that line or given in its slope-intercept form y = mx + b.