Which of the following linear equations in standard form contains points (-2,4) and (3,9)?

Question

Which of the following linear equations in standard form contains points (-2,4) and (3,9)?

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Claire 1 week 2021-11-26T04:54:56+00:00 2 Answers 0

Answers ( )

    0
    2021-11-26T04:56:16+00:00

    Answer:

    y=x+6

    Step-by-step explanation:

    If you need to find a standard linear equation from two points, you have to first find the slope, then find the y intercept.

    To find the slope, you should do the change in y over the change in x.

    that would be:

    (4-9)/(-2-3)

    (-5)/(-5)

    the slope is 1

    plug that in along with values of x and y taken from known point (3,9) to the standard equation of a linear relationship:

    y=mx+b

    m=1

    y=9

    x=3

    b=?

    9=(1)(3)+b

    9=3+b

    b=6

    The equation of the line would be y=x+6

    0
    2021-11-26T04:56:54+00:00

    Answer:

    x – y = – 6

    Step-by-step explanation:

    The equation of a line in standard form is

    Ax + By = C ( A is a positive integer and B, C are integers )

    Obtain the equation in slope- intercept form

    y = mx + c ( m is the slope and c the y- intercept )

    Calculate m using the slope formula

    m = (y₂ – y₁ ) / (x₂ – x₁ )

    with (x₁, y₁ ) = (- 2, 4) and (x₂, y₂ ) = (3, 9)

    m = \frac{9-4}{3+2} = \frac{5}{5} = 1, hence

    y = x + c ← is the partial equation

    To find c substitute either of the 2 points into the partial equation

    Using (3, 9), then

    9 = 3 + c ⇒ c = 9 – 3 = 6

    y = x + 6 ← equation in slope- intercept form

    Subtract y from both sides

    0 = x – y + 6 ( subtract 6 from both sides )

    – 6 = x – y, thus

    x – y = – 6 ← in standard form

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