Write the equation of the line in standard form

Question

through (-4,7); parallel to 3x+4y=4

Answer 1

Parallel lines have the same slope. So, let's rearrange that equation into slope-intercept form (y=mx+b) to find the line's slope:

 

3x + 4y = 4

4y = -3x + 4

y = (-3/4)x + 1

 

The slope of this line, and therefore of your line, is -3/4.

 

Now, use point-slope form to write the equation of a line with slope m = -3/4 and point (x₁, y₁) = (-4, 7):

 

y - y₁ = m(x - x₁)

y - 7 = (-3/4)(x + 4)

 

Finally, rearrange that equation so that x and y are together on one side to get standard form (Ax + By = C):

 

y - 7 = (-3/4)x - 3

y = (-3/4)x - 3 + 7

y + 3/4x = 4