which is an equation of the line that contains the points (0,2) (4,0)

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which is an equation of the line that contains the points (0,2) (4,0)

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Sophia 2 weeks 2021-10-04T09:36:26+00:00 1 Answer 0

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    2021-10-04T09:37:47+00:00

    Answer:

    Y= -1/2x+2

    Step-by-step explanation:

    First of all, remember what the equation of a line is:

    y = mx+b

    Where:

    m is the slope, and

    b is the y-intercept

    First, let’s find what m is, the slope of the line…

    The slope of a line is a measure of how fast the line “goes up” or “goes down”. A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn’t very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.

    For lines like these, the slope is always defined as “the change in y over the change in x” or, in equation form:

    So what we need now are the two points you gave that the line passes through. Let’s call the first point you gave, (0,2), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=0 and y1=2.

    Also, let’s call the second point you gave, (4,0), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=4 and y2=0.

    Now, just plug the numbers into the formula for m above, like this:

    m=

    0 – 2

    4 – 0

    or…

    m=

    -2

    4

    or…

    m=-1/2

    So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:

    y=-1/2x+b

    Now, what about b, the y-intercept?

    To find b, think about what your (x,y) points mean:

    (0,2). When x of the line is 0, y of the line must be 2.

    (4,0). When x of the line is 4, y of the line must be 0.

    Because you said the line passes through each one of these two points, right?

    Now, look at our line’s equation so far: y=-1/2x+b. b is what we want, the -1/2 is already set and x and y are just two “free variables” sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (0,2) and (4,0).

    So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.

    You can use either (x,y) point you want..the answer will be the same:

    (0,2). y=mx+b or 2=-1/2 × 0+b, or solving for b: b=2-(-1/2)(0). b=2.

    (4,0). y=mx+b or 0=-1/2 × 4+b, or solving for b: b=0-(-1/2)(4). b=2.

    See! In both cases we got the same value for b. And this completes our problem.

    The equation of the line that passes through the points

    (0,2) and (4,0)

    is

    y=-1/2x+2

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