Question

20 points! o(*￣▽￣*)\

Answer 1

Answer:

$\displaystyle y=8x$

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:

$\displaystyle m=\frac{y_2-y_1}{x_2-x_1}$

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:

$\displaystyle m=\frac{16-8}{2-1}$

Evaluate:

$\displaystyle m=\frac{8}{1}=8$

So, our slope is 8.

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

$\displaystyle y-y_1=m(x-x_1)$

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:

$\displaystyle y-8=8(x-1)$

Solve for y. Distribute the right:

$\displaystyle y-8=8x-8$

Add 8 to both sides:

$\displaystyle y=8x$

And we have our equation.

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

Answer 2

Answer:I believe its y=8x or y=8