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The equation for line r can be written as y=-1/4x+3. Line s which is parallel to lone r includes the point (-4,3). What is the equation of line s?

Respuesta :

theleangreenbean

Answer:

[tex]y=-\frac{1}{4}x+2[/tex]

Step-by-step explanation:

Hi there!

What we need to know:

  • 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 is 0)
  • Parallel lines always have the same slope

1) Determine the slope of line S using line R (m)

[tex]y=-\frac{1}{4} x+3[/tex]

We can identify clearly that the slope of the line is [tex]-\frac{1}{4}[/tex], as it is in the place of m. Because parallel lines always have the same slope, the slope of line S would also be [tex]-\frac{1}{4}[/tex]. Plug this into [tex]y=mx+b[/tex]:

[tex]y=-\frac{1}{4}x+b[/tex]

2) Determine the y-intercept of line S (b)

[tex]y=-\frac{1}{4}x+b[/tex]

Plug in the given point (-4,3) and solve for b

[tex]3=-\frac{1}{4}(-4)+b\\3=1+b[/tex]

Subtract 1 from both sides to isolate b

[tex]3-1=1+b-1\\2=b[/tex]

Therefore, the y-intercept is 2. Plug this back into [tex]y=-\frac{1}{4}x+b[/tex]:

[tex]y=-\frac{1}{4}x+2[/tex]

I hope this helps!

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