Final answer:
To determine the equation of a line that is perpendicular to a given line and has an x-intercept of 6, we take the negative reciprocal of the slope of the original line and use it to find the new slope and y-intercept for the perpendicular line.
Step-by-step explanation:
The question is asking for the equation of a line that is perpendicular to a given line and also has a specific x-intercept. To find the equation of a line that is perpendicular to another, we need to use the negative reciprocal of the slope of the given line. Since we don't have a specific slope for the given line, let's assume the slope of the given line is 'm'. Then, the slope of the perpendicular line will be '-1/m'. With an x-intercept of 6, the line will cross the x-axis at the point (6,0). Therefore, the y-intercept 'b' can be calculated using the formula 'y = mx + b' by substituting the point (6,0) into the equation. Once we calculate 'b', we will have the complete equation for the perpendicular line in the form 'Oy = mx + b'.