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Find the equation of the line through (9,-7) that is perpendicular to the line y = -x/2 - 2

Sagot :

theleangreenbean

Answer:

[tex]y=2x-25[/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, such as 2 and -1/2, 3/4 and -4/3.

1) Determine the slope (m)

[tex]y = \displaystyle -\frac{x}{2} - 2[/tex]

Rewrite the given line:

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

Now, we can clearly identify the slope to be [tex]\displaystyle-\frac{1}{2}[/tex]. Because perpendicular lines always have slopes that are negative reciprocals, the slope of the line we're currently solving for is therefore 2. Plug this into [tex]y=mx+b[/tex]:

[tex]y=2x+b[/tex]

2) Determine the y-intercept (b)

[tex]y=2x+b[/tex]

Plug in the given point (9,-7) and solve for b:

[tex]-7=2(9)+b\\-7=18+b\\b=-25[/tex]

Therefore, the y-intercept is -25. Plug this back into [tex]y=2x+b[/tex]:

[tex]y=2x+(-25)\\y=2x-25[/tex]

I hope this helps!

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