20 points! o(*￣▽￣*)\
Write a linear equation in slope-intercept form to represent the data shown in this table.
Bicycle Rental Costs
Time, x(hours) Total cost, y(dollars)
1 $8
2 $16
3 $24

Show your work.

Answer:

[tex]\displaystyle y=8x[/tex]

Step-by-step explanation:

We are given a table and we want to determine a linear equation (in slope-intercept form) that represents this table.

So, we will first need to determine the slope. We can use the slope formula:

[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Where (x₁, y₁) and (x₂, y₂) are two points.

We have three points: (1, 8), (2, 16), and (3, 24).

Let’s pick two. We can use (1, 8) and (2, 16).

So, let (1, 8) be (x₁, y₁) and let (2, 16) be (x₂, y₂). Substitute appropriately:

[tex]\displaystyle m=\frac{16-8}{2-1}[/tex]

Evaluate:

[tex]\displaystyle m=\frac{8}{1}=8[/tex]

So, our slope is 8.

Now, we can determine the equation using point-slope form:

[tex]\displaystyle y-y_1=m(x-x_1)[/tex]

Where m is our slope and (x₁, y₁) is a point.

We know that the slope is 8, so we will substitute 8 for m.

We can use any of our three points for the point. Let’s use (1, 8) for consistency. So, let (1, 8) be (x₁, y₁). Substitute appropriately:

[tex]\displaystyle y-8=8(x-1)[/tex]

Solve for y. Distribute the right:

[tex]\displaystyle y-8=8x-8[/tex]

Add 8 to both sides:

[tex]\displaystyle y=8x[/tex]

And we have our equation.

Notice that this is a direct variation or proportional equation as we don’t have a y-intercept.

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