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What is the equation of the line that is perpendicular to the given line and passes through the point (3, 4)? y = –One-thirdx + 5
y = –One-thirdx + 3
y = 3x + 2
y = 3x − 5

Question:

On a coordinate plane, a line goes through (negative 3, 2) and (0, 1). A point is at (3, 4). What is the equation of the line that is perpendicular to the given line and passes through the point (3, 4)? y = –One-thirdx + 5 y = –One-thirdx + 3 y = 3x + 2 y = 3x − 5

Option D: is the equation of the line

Explanation:

It is given that the line passes through the points and

We shall find the equation of the line that passes through the points and

Slope

Also, it is given that the line is perpendicular to the line having slope

Since, we know that if two lines are perpendicular, then the product of the two slope is equal to -1.

Thus, we have,

Thus, the slope of the line is and passes through the point

Now, we shall find the equation of the line using the formula,

Thus, we have,

Thus, the equation of the line is

Hence, Option D is the correct answer.