Question

Super easy word problem please help with question :(

Answer 1

1. The required slope m, for the context is
`m = 1.08`

2. The y-intercept in the context is
`a = y = 1052`

3. The graph is on Desmos.

Explanation:

Given:

`a = 1.08* t + 1052`

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

`y = mx + c`

Where,

m = Slope of the line.

c = y-intercept.

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

`m = 1.08\\\\c = 1052`

So ,the slope in the context of the problem is
`m = 1.08`.

and the y intercept in the context of the problem
`a = c = y = 1052`

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
`t = x = -974.07`

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