The equation of the line that is perpendicular to the given line and has an x-intercept of 6 is y = [tex]\frac{4}{3}x-8[/tex]
Perpendicular lines
Perpendicular lines follows the mathematical principle.
where
m₁ and m₂ are slopes of the lines.
A line that has a x - intercept of 6 and perpendicular to the given line can be represented as follows.
y = mx + b
where
m = slope
b = y-intercept
(-4, 4)(4, -2)
m = -2 - 4 / 4 + 4 = -6 / 8 = -3 / 4
m₁m₂ = -1
- 3 / 4 m₂ = -1
m₂ = [tex]\frac{4}{3}[/tex]
Therefore,
x-intercept of 6
0 = 6([tex]\frac{4}{3}[/tex]) + b
b = - 8
Therefore, the equation is as follows:
y = [tex]\frac{4}{3}x-8[/tex]
learn more on x-intercept here: https://brainly.com/question/16952211
