Super easy word problem with question : (

1. The required slope m, for the context is

2. The y-intercept in the context is

3. The graph is on Desmos.

Step-by-step explanation:

Given:

Where,

a is the speed of sound wave.

t is the air temperature.

This is a linear model type equation.

Can be represented in the slope intercept form  which is equal to

Where,

m = Slope of the line.

c = y-intercept.

Now if we compare the given model by slope intercept formula we get

So ,the slope in the context of the problem is .

and the y intercept in the context of the problem

For Sketching the graph we require two point

put t = 0

∴ a = 1052

Let A (1052, 0) be one point.

put a = 0

∴ t = -974.07

Let B (0, -974.07) another point.

So, the x intercept of the linear model is

Here in the graph

X axis represent temperature in degree, Fahrenheit.(t)

Y axis represent Speed of sound wave in feet per second.(a)

Scale on both axes:

1 cm = 100 feet per second on y-axis

1 cm = 100 degree Fahrenheit on x-axis

The points option A) (4,-5) and option C) (2,1) lies on the line m.

Step-by-step explanation:

The given equation of the line is

The general equation of the line is

where,

From the given equation,

It can be found that the slope of the line, m is -2/3.

The line is parallel to the given line. Therefore, their slopes are equal.

Since the two lines are parallel, their slope is also same.

The line passes through the point (-1,3).

To find the slope :

Slope =

Now, let's check the each options to find the slope is same or not.

Option A) is (-4,5) and the given point is (-1,3)

Slope =

⇒ slope =  -2/3

Therefore, the point (-4,5) could also be on the line m.

Option B) is (-3,6) and the given point is (-1,3)

Slope =

⇒ slope =  -3/2

The point (-3,6) cannot be on the line m.

Option C) is (2,1) and the given point is (-1,3)

Slope =

⇒ slope =  -2/3

Therefore, the point (2,1) could also be on the line m.

Option D) is (3,-2) and the given point is (-1,3)

Slope =

⇒ slope =  -5/4

The point (3,-2) cannot be on the line m.

Option E) is (6,-3) and the given point is (-1,3)

Slope =

⇒ slope =  -6/7

The point (6,-3) cannot be on the line m.