Answer:
The equation of the line that passes through (7, 10) and is perpendicular to the line y = yx-9 is y = -x - 3
Explanation:
To find the equation of the line that passes through the point (7, 10) and is perpendicular to the line y = yx-9, we need to determine the slope of the given line and then find the negative reciprocal of that slope.
The given line is in the form y = yx-9. By rearranging the equation, we can identify the slope of the line.
y = yx-9
y = x - 9
The slope of the given line is 1.
Since the line we want to find is perpendicular to the given line, its slope will be the negative reciprocal of 1, which is -1.
Now that we have the slope of the perpendicular line, we can use the point-slope form of a linear equation to find the equation of the line.
y - y1 = m(x - x1)
Using the point (7, 10) and the slope of -1, we substitute the values into the point-slope form:
y - 10 = -1(x - 7)
y - 10 = -x + 7
Simplifying the equation, we have:
y = -x - 3