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dimaraw [331]
3 years ago
5

Write the equation of the line for the following table of values.

Mathematics
1 answer:
Luda [366]3 years ago
5 0

Answer:

We conclude that the equation of the line is:

  • y = 5x + 1

Step-by-step explanation:

The slope-intercept form of the line equation

y = mx+b

where

  • m is the slope
  • b is the y-intercept

Given the data table

x      -3 -5 -7 -9 -11

y      -16 -26 -36 -46 -56

From the table taking two points

  • (-3, -16)
  • (-5, -26)

Determining the slope between (-3, -16) and (-5, -26)

\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}

\left(x_1,\:y_1\right)=\left(-3,\:-16\right),\:\left(x_2,\:y_2\right)=\left(-5,\:-26\right)

m=\frac{-26-\left(-16\right)}{-5-\left(-3\right)}

m=5

Thus, the slope of the line is:  m = 5

substituting m = 5 and (-3, -16) in the slope-intercept form of the line equation  to determine the y-intercept b

y = mx+b

-16 = 5(-3) + b

-16 = -15 + b

b = -16+15

b = 1

Thus, the y-intercept b = 1

now substituting m = 5 and b = 1 in the slope-intercept form of the line equation

y = mx+b

y = 5x + 1

Therefore, we conclude that the equation of the line is:

  • y = 5x + 1
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Which is a factor of the polynomial f(x) = 6x4 – 21x3 – 4x2 + 24x – 35?
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<span>I note that this problem starts out with "Which is a factor of ... "  This implies that you were given several answer choices.  If that's the case, it's unfortunate that you haven't shared them.

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Possible zeros of this poly are factors of 35:  plus or minus 1, plus or minus 5, plus or minus 7.  Use synthetic division; determine whether or not there is a non-zero remainder in each case.  If none of these work, form rational divisors from 35 and 6 and try them:  5/6, 7/6, 1/6, etc.

Provided that you have copied down the function 
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By graphing this function, I found that the graph crosses the x-axis at 7/2.  There is another root.

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         ___________________________
7/2   /   6    -21    -4    24    -35
                   21      0   -14     35           
        ----------- ------------------------------
           6        0     -4    10       0

Because the remainder is zero, 7/2 (or 3.5) is a root of the polynomial.  Thus, (x-3.5), or (x-7/2), is a factor.

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