Answer:
[tex]y=\dfrac{4}{3}x-8[/tex]
Option 3 is correct
Step-by-step explanation:
To find: The equation of perpendicular to given line and has x-intercept 6
x-intercept is on x-axis where y value is 0.
Therefore, x-intercept: (6,0)
Now we will check each point for each option.
Option 1: [tex]y=-\dfrac{3}{4}x+8[/tex]
Put x=6, y=0
[tex]0=-\dfrac{3}{4}\cdot 6+8[/tex]
[tex]0\neq\dfrac{7}{2}[/tex]
False
Option 2: [tex]y=-\dfrac{3}{4}x+6[/tex]
Put x=6, y=0
[tex]0=-\dfrac{3}{4}\cdot 6+6[/tex]
[tex]0\neq\dfrac{3}{2}[/tex]
False
Option 3: [tex]y=\dfrac{4}{3}x-8[/tex]
Put x=6, y=0
[tex]0=\dfrac{4}{3}\cdot 6-8[/tex]
[tex]0=0[/tex]
True
Option 1: [tex]y=\dfrac{4}{3}x-6[/tex]
Put x=6, y=0
[tex]0=\dfrac{4}{3}\cdot 6-6[/tex]
[tex]0\neq2[/tex]
False
Hence, The perpendicular equation is [tex]y=\dfrac{4}{3}x-8[/tex]
