Final answer:
To find the equation of line t, we need to find the slope of the given line and then find its negative reciprocal. Using the point-slope form of a line, we can find the equation of line t by plugging in the values of the point and slope. The equation of line t is y = (4/9)x + 1/3, written in slope-intercept form.
Step-by-step explanation:
To find the equation of line t that is perpendicular to the given line, we need to find the slope of the given line and then find its negative reciprocal. The given line has a slope of -9/4, so the slope of line t will be 4/9.
Using the point (-3, -1) that the line passes through, we can use the point-slope form of a line to find the equation of line t.
The point-slope form is y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.
Plugging in the values, we have y - (-1) = (4/9)(x - (-3)), which simplifies to y + 1 = (4/9)(x + 3).
Finally, we can rewrite the equation in slope-intercept form by solving for y. Distributing 4/9 to both terms inside the parentheses, we get y + 1 = (4/9)x + 4/3.
Subtracting 1 from both sides, we have y = (4/9)x + 4/3 - 1, which simplifies to y = (4/9)x + 1/3. Therefore, the equation of line t is y = (4/9)x + 1/3, written in slope-intercept form.