Final answer:
To find the equation for a line perpendicular to y = -3x - 1 and passing through the point (-9,1), we first determine the slope of the given line as -3. The slope of the line perpendicular will be the negative reciprocal of -3, which is 1/3. Then, using the point-slope form of a linear equation, we plug in the values to get y = 1/3x + 3.
Step-by-step explanation:
To find an equation for a line perpendicular to y = -3x - 1 and passing through the point (-9,1), we first need to determine the slope of the given line. The slope of the given line is -3 (the coefficient of x). The slope of the line perpendicular to the given line will be the negative reciprocal of -3, which is 1/3.
Now we can use the point-slope form of a linear equation to write the equation for the line. The point-slope form is y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope. Plugging in the values, we get y - 1 = 1/3(x - (-9)). Simplifying this equation gives us y - 1 = 1/3(x + 9). Now we can rearrange the equation to get y = 1/3x + 3.
Therefore, the equation for a line perpendicular to y = -3x - 1 and passing through the point (-9,1) is y = 1/3x + 3.