Final answer:
Parallel line: y=− 1/2x+8. Perpendicular line: y=2x+2.
Step-by-step explanation:
The subject of this question is Mathematics, specifically focusing on the algebra of straight lines and their properties, such as slope and y-intercept. When two lines are parallel, they share the same slope.
The provided equation, y = (1/2)x + 6, has a slope of 1/2. Therefore, any line that is parallel to this one must also have a slope of 1/2. The y-intercept can vary, and it is represented by the constant term in the linear equation.
The line given in the question is parallel to Line 1 but the complete equation for Line 1 is not provided. However, we understand that Line 1 must also have a slope of 1/2 to be parallel to the given line.
Your correct question is: Given an equation of a line such as y = -1/2x + 6, how can you create an equation of a line parallel and perpendicular to this line that goes through another point such as (4, 10)?