Final answer:
The equation of line r, which is perpendicular to line q with an equation of y=3x–2 and passes through the point (1,3), is y = –1/3x + 10/3.
Step-by-step explanation:
The equation of line q is y=3x–2. To find the equation of line r, which is perpendicular to line q, we need to use the negative reciprocal of the slope of line q. Since the slope (m) of line q is 3, the slope of line r will be –(1/3). The equation for a perpendicular line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. As line r passes through the point (1,3), we can substitute x=1 and y=3 into the equation y = (–1/3)x + b to solve for the y-intercept b.
Substituting the point gives us 3 = (–1/3)×1 + b, which simplifies to 3 = –1/3 + b. Adding 1/3 to both sides gives us b = 3 + 1/3 = 10/3. Therefore, the equation of line r in slope-intercept form is y = –1/3x + 10/3, which corresponds to answer choice A.