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.
<h3>What is a slope?</h3>
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.
To know more about slope, visit:
brainly.com/question/3605446
#SPJ9
