11. Suppose that the water level of a river is 34 feet after 3 days of rain and 62 feet after 10 days of rain. The river was 22 feet before the rain began.(4 points)

Question

Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.

a. What is the rate of change (slope) for this scenario? Response area

b. What is the y-intercept for this scenario? Response area

c. Write an equation for the scenario in slope-intercept form. Response area

d. Write this equation in standard form. Response area

Answer 1

a. The rate of change (slope) for this scenario can be calculated by finding the difference in water level (change in y) divided by the difference in time (change in x).

The change in water level is 62 - 34 = 28 feet.
The change in time is 10 - 3 = 7 days.

So the slope is 28 feet / 7 days = 4 feet per day.

b. The y-intercept for this scenario is the starting water level before the rain began, which is 22 feet.

c. To write the equation in slope-intercept form, we can use the slope (m) and the y-intercept (b).

The slope is 4 feet per day, and the y-intercept is 22 feet.

So the equation in slope-intercept form is y = 4x + 22.

d. To write the equation in standard form, we need to rearrange the equation to have the x and y terms on the same side and the constant term on the other side.

Starting with y = 4x + 22, we can subtract 4x from both sides to get -4x + y = 22.

So the equation in standard form is -4x + y = 22.