Question

PLEASE HELP!! I just need help with b-d!

Answer 1

b) The slope of line is 20

c) The equation in slope-intercept form is:
`\mathbf{y=20x}`

d) i) she would have travelled 1480 m after 74 s

ii) It will take 125 s to travel 2.5 km

Explanation:

Part b: Slope of Line

Slope of line can be found using formula:
`Slope=(y_2-y_1)/(x_2-x_1)`

From the table we can take any two points and find the slope.

Looking at the graph, the time is x-axis and distance is y-axis

Let we take (0,0) and (8,160)

So, we have:
`x_1=0, y_1=0, x_2=8, y_2=160`

Now finding Slope:

`Slope=(y_2-y_1)/(x_2-x_1)\\Slope=(160-0)/(8-0) \\Slope=(160)/(8)\\Slope=20`

So, the slope of line is 20

Part c) Find the equation in slope-intercept form

The general equation of slope-intercept form is:
`y=mx+b` where m is slope and b is y-intercept

We have found slope, m = 20

We need to find y-intercept.

y-intercept can be found by putting x-axis (time) equal to zero and check what the y-axis (distance) is:

So, when x =0, y=0

So, y-intercept = 0

The equation will be:

`y=mx+b\\y=20x+0\\y=20x`

The equation in slope-intercept form is:
`\mathbf{y=20x}`

Part d)

Part i) How far will she have travelled after 74 s

We are given time (x) = 74 s

We need to find distance i.e. y:

Using the equation:
`\mathbf{y=20x}`

Put x = 74

`y=20x\\y=20(74)\\y=1480`

So, she would have travelled 1480 m after 74 s

Part ii) How long will it take to travel 2.5 km

We are given distance (y) = 2.5 km

We need to find time i.e. x:

Using the equation:
`\mathbf{y=20x}`

Since distance is given in meters but here it is in km

So converting 2.5 km into m

We know that 1 km = 1000m

So, 2.5 km = 2500 m

Now finding time:

`y=20x\\2500=20(x)\\x=(2500)/(20)\\x=125`

So, It will take 125 s to travel 2.5 km