Question

What is the equation of the line that is perpendicular to the given line and passes though the point (3,0)? ......What is the answer.....

Answer 1

Answer: The correct option is (D)
`5x-3y=15.`

Step-by-step explanation: We are given to find the equation of a line that is perpendicular to the graphed line and passes through the point (3, 0).

From the graph, we note that

the graphed line passes through the points (2, -1) and (-3, 2).

The SLOPE of a straight line passing through the points (a, b) and (c, d) is given by

`m=(d-b)/(c-a).`

So, the slope of the graphed line is

`m=(2-(-1))/(-3-2)\\\\\Rightarrow m=-(3)/(5).`

We know that the product of the slopes of two perpendicular lines is -1. So, if m' is the slope of a line perpendicular to the graphed line, then

`m* m'=-1\\\\\Rightarrow -(3)/(5)* m'=-1\\\\\Rightarrow m'=(5)/(3).`

Since the line with slope m' passes through the point (3, 0), so its equation will be

`y-0=m'(x-3)\\\\\\\Rightarrow y=(5)/(3)(x-3)\\\\\Rightarrow 3y=5x-15\\\\\Rightarrow 5x-3y=15.`

Thus, the required equation of the perpendicular line is
`5x-3y=15.`

Option (D) is CORRECT.