If your given points like (3, 2) (7,6) and are told to find the line perpendicular to the point (9,8) how could you solve it without graphing?
To find the line perpendicular to a given line without graphing, you can follow these steps:
1. Identify the slope (m) of the given line. The slope of a line passing through two points (x1, y1) and (x2, y2) can be determined using the formula: m = (y2 - y1) / (x2 - x1).
In this case, the given line passes through points (3, 2) and (7, 6). Using the formula, the slope of the given line is:
m = (6 - 2) / (7 - 3) = 4 / 4 = 1.
2. Determine the negative reciprocal of the slope. For any line that is perpendicular to another, its slope is the negative reciprocal of the original line's slope. The negative reciprocal is obtained by flipping the fraction and changing its sign.
In this case, the negative reciprocal of 1 is -1.
3. Use the negative reciprocal slope (m) and the given point (9, 8) to determine the equation of the perpendicular line using the point-slope form.
The point-slope form of a line is given by the equation: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Plugging in the values, we have:
y - 8 = -1(x - 9)
y - 8 = -x + 9
y = -x + 17
So, the equation of the line perpendicular to the line passing through (3, 2) and (7, 6), and passing through (9, 8), is y = -x + 17.