Question

1. A relation is plotted as a linear function on the coordinate plane starting at point A (0,3) and ending at point B (2,7). What is the rate of change for the linear function?

2. A relation is plotted as a linear function on the coordinate plane starting at point A (0,3) and ending at point B (2,7). What is the initial value for the linear function?


3. The graph shows the miles per gallon of gasoline a car uses on a trip. What is the rate of change? What does the rate of change represent?

4. Determine if each function is linear or nonlinear.
y=x
3x+y=12
Y=3x^2-4x+2
y=3x-4

Answer 1

1. The rate of change is 2.

2. Initial value is 3.

3. The rate of change is 25.

4. y = x ..... It is classified as a linear function

3x + y = 12 ........ It is classified as a linear function.

y = 3x² - 4x + 2 ........ It is a non-linear function.

y = 3x - 4 ........It is classified as a linear function.

Explanation:

1. A relation is plotted as a linear function on the coordinate plane starting at point A (0,3) and ending at point B (2,7).

Therefore, the rate of change for the linear function i.e. the slope of the equation is
`(7 - 3)/(2 - 0) = 2` (Answer)

2. A relation is plotted as a linear function on the coordinate plane starting at point A (0,3) and ending at point B (2,7).

Therefore, the equation of the linear function will be

`(y - 7)/(7 - 3) = (x - 2)/(2  - 0)`

⇒ (y - 7) = 2(x - 2)

⇒ y - 7 = 2x - 4

⇒ y = 2x + 3

This equation is in slope-intercept form and the initial value i.e. the y-intercept is 3. (Answer)

3. See the graph given.

The points (0,0) and (2,50) through which the graph passes.

So, the rate of change of the function i.e. slope of the function will be

`(50 - 0)/(2 - 0) = 25`

This rate of change of 25 miles per gallons means the distance traveled by car in miles using 1 gallon of fuel. (Answer)

4. y = x ..... It is classified as a linear function

3x + y = 12 ........ It is classified as a linear function.

y = 3x² - 4x + 2 ........ It is a non-linear function.

y = 3x - 4 ........It is classified as a linear function. (Answer)