Write the equation of a line in slope-intercept form that is perpendicular to the line and passes through the point (-9, 4).
We need the slope of one of the lines.
To find the equation of a line in slope-intercept form that is perpendicular to a given line, we need to determine the slope of the given line and then find the negative reciprocal of that slope.
Let's begin by finding the slope of the given line. However, you didn't provide the equation of the given line, so we will assume it is in the form of y = mx + b, where m is the slope of the line. Please provide the equation of the given line if you have it.
Once we have the slope of the given line, we can find the negative reciprocal by flipping the fraction and changing the sign. Let's say the slope of the given line is m. The negative reciprocal would be -1/m.
Now, we have the slope of the line perpendicular to the given line. We also have a point that this line passes through (-9, 4). We can use the slope-intercept form of a line, y = mx + b, to find the equation of the line.
Plugging in the slope (-1/m) and the coordinates of the point (-9, 4) into the equation, we have:
4 = (-1/m)(-9) + b
Simplifying:
4 = 9/m + b
To find b, we need to solve for it by rearranging the equation:
b = 4 - 9/m
Therefore, the equation of the line in slope-intercept form that is perpendicular to the given line and passes through the point (-9, 4) is:
y = (-1/m)x + (4 - 9/m)