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theleangreenbean

Linear Equations

Typically, linear equations are written in slope-intercept form:

[tex]y=mx+b[/tex]

  • m = slope
  • b = y-intercept (the value of y when the line crosses the y-axis)

To find the equation of a line given a point and the slope:

  1. Plug the slope into y=mx+b as m
  2. Plug the point into y=mx+b as (x,y)
  3. Solve for b
  4. Plug b back into y=mx+b along with m

Solving the Question

We're given:

  • [tex]m=\dfrac{1}{5}[/tex]
  • Passes through (-5,-4)

[tex]y=mx+b[/tex]

⇒ Plug in the slope, [tex]\dfrac{1}{5}[/tex]:

[tex]y=\dfrac{1}{5}x+b[/tex]

⇒ Plug in the point (-5,-4) and solve for b:

[tex]-4=\dfrac{1}{5}(-5)+b\\\\-4=-1+b\\\\b=-3[/tex]

⇒ Therefore, the y-intercept of the line is -3. Plug this back into our original equation as b:

[tex]y=\dfrac{1}{5}x-3[/tex]

Answer

[tex]y=\dfrac{1}{5}x-3[/tex]

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