Question is in description.

Question

^{Write an equation for the line parallel to the line 1/4x + 3y = −1 through the point (0, 1). Please enter your answer in slope-intercept form or standard form}

Answer 1

The line:   1/4x + 3y = −1  is also the line:

         x + 12y = -4             [Standard Form; multiply everything by 4]

 

All parallel lines have the same slope, so they have the equation:

         x + 12y = D      [and we need point (0,1) to find D]

      0 + 12(1) = D

             D=12

 

The parallel line has the equation (in Standard Form):

         x + 12y = 12

Answer 2

First let's get the slope of our original equation:

¹/₄ x + 3y = -1

3y = -¹/₄ x - 1

y = -¹/₁₂ x - ¹/₃

If the line is parallel, then we already have the slope: -¹/₁₂. We also have a point: (0, 1). This means we can use the point-slope formula and convert that into slope-intercept form:

y - y₁ = m(x - x₁)

y - 1 = -¹/₁₂(x - 0)

y - 1 = -¹/₁₂ x 

y = -¹/₁₂ x + 1