Respuesta :

theleangreenbean

Answer:

[tex]y=-3x+8[/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 the line crosses the y-axis)
  • Parallel lines always have the same slope

1) Determine the slope (m)

[tex]y = 4 - 3x\\y = -3x+4[/tex]

Given this equation, we can identify the slope to be -3 since it's in the place of m in [tex]y=mx+b[/tex].

Because parallel lines have the same slope, -3 is therefore the slope of the line we're currently solving for. Plug this into [tex]y=mx+b[/tex]:

[tex]y=-3x+b[/tex]

2) Determine the y-intercept (b)

[tex]y=-3x+b[/tex]

Plug in the given point (1,5) and solve for b:

[tex]5=-3(1)+b\\5=-3+b\\8=b[/tex]

Therefore, the y-intercept is 8. Plug this back into [tex]y=-3x+b[/tex]:

[tex]y=-3x+8[/tex]

I hope this helps!

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