Algebra 2 help

Question

Write the equation of the line with a slope of -5 and a y-intercept of (0,3)


Write the equation of the line with a slope of -1/3 and passing through the point (6, -4).


Write the equation of the line passing through the points (0, -4) and (-2, 2).



Write the equation of the line passing through the points (-6,1) and (-4,2).



Write the equation of the line with an undefined slope, passing through the point (2, 5). Hint: refer back to lesson 4.04 for help with this one.

Answer 1

Write the equation of the line with a slope of -5 and a y-intercept of (0,3)
    Using the slope-intercept form of the equation of a line (y=mx+b), the equation is:

      y = -5x + 3

Write the equation of the line with a slope of -1/3 and passing through the point (6, -4).

    You may either just solve for b, or use the point-slope form of the equation.

       y = (-1/3)x + b

       -4 = (-1/3)(6) + b

       -4 = -2 + b

       -2 = b

   The equation is:  y = (-1/3)x – 2

    Check:  Is -4 = (-1/3)(6) -2   ?yes 

Write the equation of the line passing through the points (0, -4) and (-2, 2).
    The point-slope form is needed now:

     (y-y₁) = ( (y₂-y₁)/(x₂-x₁) )(x-x₁)

    y-(-4) = ( (2-(-4))/(-2-0) )(x-0)

    y+4 = (6/(-2))x

    y +4 = -3x

    y = -3x-4

Check:

   Is  -4=-3(0)-4   ?yes

   Is  2=-3(-2)-4   ?yes

Write the equation of the line passing through the points (-6,1) and (-4,2).
    The point-slope form is needed again (and if you keep using this, you will be tested on it):

     (y-y₁) = ( (y₂-y₁)/(x₂-x₁) )(x-x₁)

     (y-1) = ( (2-1)/(-4-(-6)) )(x-(-6))

     y-1 = (1/2)x+3

     y = (1/2)x + 4

Check:

  Is  1=(1/2)(-6)+4   ?yes

  Is  2=(1/2)(-4)+4   ?yes

Write the equation of the line with an undefined slope, passing through the point (2, 5). Hint: refer back to lesson 4.04 for help with this one.

   Neither the slope-intercept form nor the point-slope form is helpful here (since they both use “slope” which is undefined).  The Standard Form of the equation of a line (Ax+By=C) is useful:

      x=2      [slope m=(–A/B) is undefined because B=0; line is vertical]