Final answer:
To find the equation of the line that is perpendicular to the given line and has an x-intercept of 6, we need to determine the slope of the given line. The equation of the perpendicular line is y = -1/3x + 2.
Step-by-step explanation:
To find the equation of the line that is perpendicular to the given line and has an x-intercept of 6, we need to determine the slope of the given line. Since the slope of a line perpendicular to another line is the negative reciprocal of the slope of the given line, we can find the slope of the perpendicular line by taking the negative reciprocal of the slope of the given line.
The given line has a slope of 3, so the slope of the perpendicular line is -1/3. We can use the slope-intercept form of a linear equation, y = mx + b, with the x-intercept of 6 to find the equation of the perpendicular line.
Plugging in the values, we have: y = -1/3x + b. Since the x-intercept is 6, we know that when x = 6, y = 0. Plugging in these values, we can solve for the y-intercept:
0 = -1/3(6) + b, 0 = -2 + b, b = 2.
Thus, the equation of the line that is perpendicular to the given line and has an x-intercept of 6 is y = -1/3x + 2.