x y

-2 80
-1 70
2 40
5 10

Answer the questions using the table.

(3 points)
the rate of change =


the y−intercept =

the equation of the line in slope intercept form is


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1 answer

To analyze the data in the table and answer the questions, we can first identify that we have a set of points:

  1. \((-2, 80)\)
  2. \((-1, 70)\)
  3. \((2, 40)\)
  4. \((5, 10)\)

1. To find the rate of change (slope):

The rate of change (slope) \( m \) can be calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Let's use the first two points \((-2, 80)\) and \((-1, 70)\):

\[ m = \frac{70 - 80}{-1 - (-2)} = \frac{-10}{1} = -10 \]

Thus, the rate of change is \(-10\).

2. To find the y-intercept:

Using one of the points and the slope, we can express it in point-slope form and then convert it to slope-intercept form \(y = mx + b\).

From our earlier calculation, the slope \(m = -10\). Using the point \((-1, 70)\):

Using the linear equation form: \[ y - y_1 = m(x - x_1) \] Substituting the slope and the point: \[ y - 70 = -10(x + 1) \] Expanding it out: \[ y - 70 = -10x - 10 \] \[ y = -10x + 60 \] So, the y-intercept \(b = 60\).

3. The equation of the line in slope-intercept form \(y = mx + b\):

From our calculations, the slope \(m = -10\) and the y-intercept \(b = 60\). The equation of the line is: \[ y = -10x + 60 \]

Summary of Answers:

  • The rate of change = \(-10\)
  • The y-intercept = \(60\)
  • The equation of the line in slope-intercept form is \(y = -10x + 60\)