Answer:
[tex]y=2x-2[/tex]
Step-by-step explanation:
Hi there!
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x=0)
Perpendicular lines always have slopes that are negative reciprocals. For example, 2 and -1/2. 3/4 and -4/3.
To determine whether a line is perpendicular to [tex]x + 2y = 16[/tex], we must first determine its slope. Rearrange the given equation into slope-intercept form:
[tex]x + 2y = 16\\\\2y =-x+ 16\\\\y=\displaystyle -\frac{1}{2}x +\frac{16}{2} \\\\y=\displaystyle -\frac{1}{2}x +8[/tex]
From this, we can clearly tell that the slope (m) of the line is [tex]\displaystyle -\frac{1}{2}[/tex].
The negative reciprocal of [tex]\displaystyle -\frac{1}{2}[/tex] is 2. Therefore, the slope of a perpendicular line would be 2.
Therefore, the correct answer option would be [tex]y=2x-2[/tex].
I hope this helps!
