Final answer:
The equation y - y₁ = m⋅(x - x₁) defines a line perpendicular to a given line, where (x₁, y₁) is the point of intersection, and m⋅ is the perpendicular slope. The slope represents the steepness of the line, and the y-intercept indicates the point where the line crosses the y-axis.
Step-by-step explanation:
The equation of a line perpendicular to another line with a given slope passing through a specific point is given by y - y₁ = m⋅(x - x₁), where (x₁, y₁) is the point of intersection (or the point through which the new perpendicular line passes), and m⋅ is the perpendicular slope. Hence, the correct answers are B) Initial point and D) Initial slope. To find the perpendicular slope (m⋅), you take the negative reciprocal of the original line's slope. This change in slope indicates a slope that is perpendicular to the original line.
When constructing linear equations, the slope and the y-intercept are essential. The slope (m) defines the steepness or incline of the line, and it is calculated as the rise over run, signifying the change in y (vertical axis) for a unit change in x (horizontal axis). The y-intercept (b), on the other hand, tells you at what y value the line intersects the y-axis, which is the starting point of the plot line on the y-axis.