Question

What is the equation of the line that is perpendicular to the given line and passes through the point (3, 4)?

A. y = –x + 5
B. y = –x + 3
C. y = 3x + 2
D. y = 3x − 5

Answer 1

The correct answer option is D. y = 3x - 5.

Explanation:

We are given a graph of a straight line and we are to find the equation of a line which is perpendicular to this line and passes through the point.

Firstly, we will find the slope of the line using any two points on it.

`(-3, 2) (0, 1)`

`Slope = (2-1)/(-3-0) =-(1)/(3)`

Since the slope of a perpendicular line is a negative reciprocal of the given line so our required slope is 3.

Also, we know that the standard equation of a line is given by:

`y=mx+c`

So substituting the values of the given point (3, 4) and the slope to find the y-intercept:

`4=3(3)+c`

`c=-5`

Therefore, the equation of this line is y = 3x - 5.

Answer 2

Answer: option D.

Explanation:

The equation of the line in Slope-intercerpt form is:

`y=mx+b`

Where "m" is the slope of the line and "b" is the intersection of the line with the y-xis.

The slopes of two perpendicular lines are negative reciprocals. Then, you need to find the slope of the line given in the graph, with the formula:

`m=(y_2-y_1)/(x_2-x_1)`

Then, this is:

`m=(1-2)/(0-(-3))=-(1)/(3)`

Then the slope of the other line is:

`m=3`

Substittute the point (3,4) into
`y=mx+b` and solve for "b":

`4=3(3)+b\\4-9=b\\-5=b`

Substituting you get that the equation of this line is:

`y=3x-5`