What is the equation in slope-intercept form of the linear function represented by the table? Х y -5 14 -2

Question

What is the equation in slope-intercept form of the linear function represented by the table?
Х
y
-5
14
-2
11
1
8
4
5

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Đan Thu 5 years 2021-07-29T09:07:28+00:00 1 Answers 96 views 0

Answers ( )

  1. niczorrrr
    0
    2021-07-29T09:08:50+00:00
    Reply

    Answer:

    y = -x + 9

    Step-by-step explanation:

    You are given (-5,14), (-2,11), (1,8), and (4,5).  Your first objective is to find the slope.

    Slope is delta y divided by delta x – the amount of height the graph gains divided by the amount of horizontal length the graph gains.  Take any two points and plug it into this: \frac{y_{2}-y_{1} }{x_{2}-x_{1}}.

    i.e. (-2,11) and (4,5): \frac{11-5}{-2-4} which is \frac{6}{-6}, or -1.  Thus, the slope is -1.

    We now have y = -1(x) + b, or just y = -x + b.

    Next, find the y-intercept.  Set the value of x to 0, as the y-intercept is found along the y-axis, which is at the horizontal center of the graph, 0.  We now know that the y-intercept is (0,y).  To find the y-value, plug one of the coordinate pairs of choice into x and y.

    i.e. (-5,14): 14 = (-1)(-5) + b

    14 = 5 + b

    14 – 5 = 5 + b – 5

    9 = b

    So, the y-intercept is (0,9).

    Finally, the equation is:

    y = -x + 9

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