Question

Compare the linear functions expressed by the equation, y = –x + 3, and by data in the table.

Answer 1

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.

Answer 2

Answer:

When a linear function is expressed in different forms, its slope and y-intercept remain the same. The slope from the equation is -1, and the y-intercept from the equation is 3. The slope from the table is -1, and the y-intercept from the table is −3. These are not the same functions.

Step-by-step explanation:

sample response