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

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4 Answers

Hi, Haley.

Parallel lines have the same slope. So let's write the first equation in slope-intercept form:

4x + 2y = 8

2y = -4x + 8

y = -2x + 4

The slope is -2. To find the other line, use -2 for the slope and substitute (-1,5) in for x and y into the point-slope formula:

y - y1 = m( x - x1)

y - 5 = -2(x + 1)

y - 5 = -2x - 2

y = -2x + 3

Hope this helps!

 

Another way:

1. Simplify the equation by dividing both sides by 2 to get the basic form of a line // to the given line:

2x+y = C

2. Plug in (-1, 5) to get 2(-1)+5 = C => C = 3, and 2x+y = 3

3. Solve for y to get the slope-intercept form: y = -2x+3

Parallel simply means that the two lines have the same slope.  First, we'll put the given line into slope intercept form, to make things easy:

4x+2y=8

2y=8-4x

y=4-2x (or, in y=mx+b form: y=-2x+4)

The slope of this line (as well as the line you're solving for) is -2.  Now, all you need to do is find the y-intercept of your unknown line.  Since we have a point to plug in to a slope intercept equation, we can use these values to find the y-intercept.

y=5, x=-1, m=-2, b=?

5=(-2)(-1)+b

5=2+b

b=3

Now that we have the slope and y-intercept of the line, you know your equation: y=-2x+3

Parallel lines have the same slope. Since you need to find the slope-intercept form of a line parallel to the given line, convert 4x + 2y = 8 into slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

4x+ 2y = 8

2y = -4x + 8

y = -2x + 4   (m = -2)

Next, use the point-slope equation with the given point:

y - y1 = m(x - x1)

y - 5 = -2(x - (-1)), or 

y - 5 = -2(x + 1)

expand the right side, and then add 5 to both sides:

y - 5 + 5 = -2x - 2 + 5

or:

y = -2x + 3

(Check by substituting -1 for x, and 5 for y:  5 = -2(-1) + 3, which is true)