Final answer:
To determine the equation of line u which is perpendicular to line t with an equation y = – 3x – 9 and passes through the point (6, – 3), we calculate the negative reciprocal of the slope of line t, which is 1/3, and use the point-slope formula. The final equation of line u is y = ⅓x + 1.
Step-by-step explanation:
The equation of line t is given by y = – 3x – 9. To find the equation of line u that is perpendicular to line t and passes through point (6, – 3), we need to first determine the slope of line u. Since line u is perpendicular to line t, the slope of line u will be the negative reciprocal of the slope of line t. For line t, the slope (m) is – 3. Therefore, the slope of line u will be 1/3. Using the point-slope form, we can write the equation for line u as y – y1 = m(x – x1), where (x1, y1) is the point (6, – 3) and m is 1/3. Substituting the values, we get:
y – (– 3) = (1/3)(x – 6)
Simplifying this equation, we get:
y + 3 = ⅓x – 2
Finally, simplifying further, the equation of line u is:
y = ⅓x + 1