To find the equation for line m, that is perpendicular to line k, we will take the steps below:
First, find the slope of line k from the graph given
To find the slope, locate the coordinates of any given 2 points from the line.
we have;
(4, 0) and (0, 3)
From the points above:
x₁= 4 y₁=0 x₂=0 y₂=3
slope = y₂-y₁ /x₂- x₁
substitute the values of the coordinate into the formula above
slope = 3 - 0 / 0 -4
= 3/ -4
= - 3/4
slopes of perpendicula equations are given by;
m₁m₂= -1
let m₁ be slope of k and m₂ be slope of m
(-3/4)m₂ = -1
multiply both-side of the equation by -4/3
m₂ = 4/3
The above is the slope of line M
Next, is to find the intercept of line M
y=mx + b