Maths-
General
Easy

Question

# Find the equation of line that passes through the point (2, -9) and which is perpendicular to the line x = 5.

## The correct answer is: y = - 9

### Hint:-1. Slope of verticle lines are undefined & slop of horizontal lines are 0.2. Slopes of Perpendicular lines are negative reciprocals of each other.3. Equation of a line in slope point form is-(y-y1) = m (x-x1)Step-by-step solution:-Let l be the line for which slope is to be found.The given equation of line x = 5 represents a verticle line (because its y-coordinate = 0)Now, line l is perpendicular to the given line (x = 5).∴ line l is a horizontal line i.e. parallel to x-axis.Slope of a horizontal line i.e. parallel to x-axis is always 0∴ Slope of line l = m = 0 …...................................................................................................... (Equation i)We are given that line l passes through the point (2,-9) and we know its slope.i.e. x 1 = 2 & y1 = -9 & m = 0We can use slope point form of an equation to find the equation of line l- (y - y1) = m (x - x1)∴ [y - (- 9)] = 0 (x - 2)∴ y + 9 = 0∴ y = - 9Final Answer:-∴ Equation of the given line is y = -9.

Use the perpendicular line formula to determine whether two given lines are perpendicular. For example, when the slope of two lines is given to compare, we can use the perpendicular line's formula. A 90-degree angle is created by two lines that are perpendicular to one another.
Slope exists on every line. Because it shows how quickly our line is rising or falling, the slope of a line reveals how steep a line is. Mathematically, the slope of a line is known as the ratio of change in the line's y-value to the change in its x-value.
¶A line's slope can be determined using its two points (x1, y1) and (x2, y2). The formula (y2 - y1) / is used to find the change in y and divided by the change in x. (x2 - x1).