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

Question

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luisejr77 luisejr77 · Answer 1 · 2019-04-26T22:30:28+02:00

Answer: option D.

Step-by-step explanation:

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

[tex]y=mx+b[/tex]

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:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Then, this is:

[tex]m=\frac{1-2}{0-(-3)}=-\frac{1}{3}[/tex]

Then the slope of the other line is:

[tex]m=3[/tex]

Substittute the point (3,4) into [tex]y=mx+b[/tex] and solve for "b":

[tex]4=3(3)+b\\4-9=b\\-5=b[/tex]

Substituting you get that the equation of this line is:

[tex]y=3x-5[/tex]

alinakincsem alinakincsem · Answer 2 · 2019-04-26T22:38:20+02:00

Answer:

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.

[tex](-3, 2) (0, 1)[/tex]

[tex]Slope = \frac{2-1}{-3-0} =-\frac{1}{3}[/tex]

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:

[tex]y=mx+c[/tex]

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

[tex]4=3(3)+c[/tex]

[tex]c=-5[/tex]

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