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

option D.

Step-by-step explanation:

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

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:

Then, this is:

Then the slope of the other line is:

Substittute the point (3,4) into and solve for "b":

Substituting you get that the equation of this line is:

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

Step-by-step 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.

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:

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

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