How do you find the slope intercept form of the equation of the line that passes through (-1, 5) and is parallel to #4x+2y=8#?

Question

Nathan Axel · Accepted Answer

The equation of the line in slope intercept form is #y=-2x+3#.

The slope of the line #4x+2y=8 or 2y= -4x+8 or y= -2x+4# is #-2#(obtained by comparing with the standard form of equation #y=mx+c#) Parallel lines have same slope . Thus line passing through #(-1,5)# , parallal to the line #y= -2x+4# has slope #m=-2# So the equation of the line in slope intercept form is #y=-2x+c# The point #(-1,5)# is on the line , so it satisfies the equation #y=-2x+c :. 5 = -2* -1 + c or c=5-2=3#. Hence the equation of the line is #y=-2x+3#. [Ans]

Eva Abramson · Answer

undefined To find the slope-intercept form of the equation of a line passing through a given point and parallel to another line, follow these steps:

1. Find the slope of the given line. For this, rewrite the given line in the form y = mx + b, where m is the slope:
   4x + 2y = 8
   2y = -4x + 8
   y = -2x + 4
   The slope of the given line is -2.

2. Since the line you're looking for is parallel, it will have the same slope as the given line. So, the slope of the line you're looking for is also -2.

3. Use the point-slope form of the equation of a line, y - y1 = m(x - x1), where (x1, y1) is the given point (-1, 5) and m is the slope (-2):
   y - 5 = -2(x - (-1))
   y - 5 = -2(x + 1)
   y - 5 = -2x - 2
   y = -2x + 3

So, the equation of the line that passes through (-1, 5) and is parallel to 4x + 2y = 8 is y = -2x + 3.