Question

Find the equation of the line that and I [] is perpendicular to the line y = 3x - 1 passes through the point (7,4).​

Answer 1

The equation of the line that goes through the point (7,4) and is perpendicular to the line y = 3x - 1 is y = -1/3 x + 7.

What is a slope?

The slope of a line is found by dividing the "vertical change" by the "horizontal change" between (any) two distinct places on the line. The ratio is sometimes stated as a quotient ("rise over run"), yielding the same value each time.

Given,

The line L₁ equation: y = 3x - 1

Line L intersects the point (x₁, y₁) = (7,4)

To determine the equation of line L.

The equation of a line whose slope and point of intersection are known is given by:

y-y₁ = m (x - x₁)

Where m is the slope of the line and (x₁, y₁) is the point it passes through.

Let L be our needed line.

We've been told that (x₁, y₁) = (7,4).

We also know that the line L is perpendicular to another line L₁, whose equation is:

y = 3x - 1

As a result, the slope of line L₁ is m₁ = 3.

= -1 3m = -1/3 m = -1/3

As a result, the equation for the required line is: y - y₁= m (x - x₁)

y-4 = -1/3(x-7)

3(y - 4) = -(x - 7)

3y-14 =7-x

3y = 14 + 7 - x

3y = - x + 21

y = -1/3 x + 7.

This is the required line equation.

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