contestada

Compare the linear functions expressed by the equation, y = –x + 3, and by data in the table.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 4, negative 2, 1, 3. Column 2 is labeled y with entries 1, negative 1, negative 4, negative 6.
Explain how to determine if these two are the same function expressed in different ways

Respuesta :

Edufirst

Answer:

  • The two linear equations are not the same, because have different y-intercept, but are parallel because have the same slope.

Explanation:

1. The equation y = –x + 3 is in the slope-intercept form.

The general slope-intercept form is: y = mx + b, where m is the slope and b is the y-intercept.

If two linear equations have the same slope (m) and y-intercept (b) they represent the same function.

By visual inspection, the slope and y-intercepts of y = –x + 3 are:

  • slope: m = y = –1
  • y-intercept: b = 3

2. Table

    x       y

   -4       1

   -2      -1

    1       -4

    3      -6

Calculate the slope:

  • slope = rise/run = Δy/Δx

  • (-1 - 1) / (-2 - (-4) ) = -1

  • (-4 - (-1) ) / (1 - (-2) ) = -1

  • (-6 - (-4) ) / (3 - 1) = -1

Thus, this function has a constant rate of change Δy/Δx, or slipe,  equal to slope of y = - x + 3.

What about the y-intercept?

You can calculate it using any point from the table. Using (1, -4):

  • y = mx + b
  • -4 = -1(1) + b
  • -4 = -1 + b
  • -4 + 1 = b
  • -3 = b
  • b = - 3

And the equation is y = - x - 3.

In conclusion the two linear equations are not the same, because they have different y-intercept, but are parallel because have the same slope.

fichoh

The value of the function given and that calculated from the table aren't the same, hence we can conclude that the functions are different.

  • The given linear function : y = - x + 3 - - - (1)

The table given

X _____ Y

-4 _____ 1

-2 _____ -1

1 _____ - 4

3 _____ - 6

From the table, we could find the linear function in the form : y = mx + c

  • The slope, m = (y2 - y1) ÷ (x2 - x1)

  • Slope , m = (-6 - 1) ÷ (3 - (-4)) = - 7 ÷ 7 = - 1

  • y = - x + c

  • Take any value of x and y and solve for the intercept, c

  • Taking (-4, 1)

  • 1 = - (-4) + c

  • 1 = 4c

  • c = 1/4

  • y = - x + 1/4 ----(2)

Comparing the two functions ; we can see that they are different, hence, the two functions aren't the same.

Learn more :https://brainly.com/question/15696498

Otras preguntas