Question

4a. Explain how we can tell that this graph represents the give

Answer 1

a) the slope is 250

b)for every mile ( along thail) the hikers progress 250 meters ( elevation)

c)y=250x+500

3d)yes, the equation y-250x=500 represents the same relationship

Step-by-step explanation

Step 1

slope of the line.

the slope of a line is given by the expression

`\begin{gathered} slope=(\Delta y)/(\Delta x)=(y_2-y_1)/(x_2-x_1) \\ \text{where} \\ P1(x_1,y_1)\text{ and} \\ P2(x_2,y_2) \\ are\text{ 2 points from the line} \end{gathered}`

then

pick up two poins from the line

`\begin{gathered} \text{let} \\ P1(0,500) \\ P2(2,1000) \end{gathered}`

replace in the expression

`\begin{gathered} slope=(y_2-y_1)/(x_2-x_1) \\ \text{slope}=(1000-500)/(2-0)=(500)/(2)=250 \end{gathered}`

so, the slope is 250

Step 2

what does the slope tell use about this situation

as the slope is rate of change

`\begin{gathered} slope=(\Delta y)/(\Delta x) \\ \text{replace the units ( check the a}\xi s) \\ \text{slope}=\text{ 250}\frac{ft}{\text{miles}} \end{gathered}`

so, the slope tell us

for every mile ( along thail) the hikers progress 250 meters ( elevation)

Step 3

equation:

to find the equation we can use the point slope equation

`\begin{gathered} y-y_1=m(x-x_1) \\ \text{where m is the slope} \\ \text{and} \\ P1(x_1,y_1) \end{gathered}`

replace

`\begin{gathered} y-y_1=m(x-x_1) \\ y-500=250(x-0) \\ y-500=250x \\ \text{add 500 in both sides} \\ y=250x+500 \end{gathered}`

Step 4

finally.

Does the equation y-250x=500 represent the same relationship?

if we start from

`y=250x+500`

then, we apply the subtraction property of equality ( which does not affect the function)

so

subtract 250 x in both sides

`\begin{gathered} y=250x+500 \\ \text{subtract 250 x in both sides} \\ y-250x=250x+500-250x \\ y-250x=500 \end{gathered}`

so

yes, the equation y-250x=500 represents the same relationship

I hope this helps you