Respuesta :

theleangreenbean

Answer:

[tex]y=-\frac{1}{2} x+\frac{7}{2}[/tex]

Step-by-step explanation:

Hi there!

What we need to know:

  • 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 is 0)
  • Perpendicular lines always have slopes that are negative reciprocals (ex. 2 and -1/2, 5/6 and -6/5, etc.)

1) Determine the slope (m)

[tex]y=2r-7[/tex]

From the given equation, we can identify clearly that 2 is in the place of m, making it the slope. The negative reciprocal of 2 is -1/2, so therefore, the slope of a perpendicular line would be -1/2. Plug this into [tex]y=mx+b[/tex]:

[tex]y=-\frac{1}{2} x+b[/tex]

2) Determine the y-intercept (b)

[tex]y=-\frac{1}{2} x+b[/tex]

Plug in the given point (-5,6) and solve for b

[tex]6=-\frac{1}{2} (-5)+b\\6=\frac{5}{2}+b[/tex]

Subtract 5/2 from both sides to isolate b

[tex]6-\frac{5}{2}=\frac{5}{2}+b-\frac{5}{2}\\\frac{7}{2} =b[/tex]

Therefore, the y-intercept of the line is [tex]\frac{7}{2}[/tex]. Plug this back into [tex]y=-\frac{1}{2} x+b[/tex]:

[tex]y=-\frac{1}{2} x+\frac{7}{2}[/tex]

I hope this helps!

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