Answer:
1. The required slope m, for the context is[tex]m = 1.08[/tex]
2. The y-intercept in the context is [tex]a = y = 1052[/tex]
3. The graph is on Desmos.
Step-by-step explanation:
Given:
[tex]a = 1.08\times t + 1052[/tex]
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
[tex]y = mx + c[/tex]
Where,
m = Slope of the line.
c = y-intercept.
Now if we compare the given model by slope intercept formula we get
[tex]m = 1.08\\\\c = 1052[/tex]
So ,the slope in the context of the problem is [tex]m = 1.08[/tex].
and the y intercept in the context of the problem [tex]a = c = y = 1052[/tex]
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 [tex]t = x = -974.07[/tex]
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
