Are 1/2 and 2/4 proportional?
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Answer:
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:
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:
Evaluate:
So, our slope is 8.
Now, we can determine the equation using point-slope form:
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:
Solve for y. Distribute the right:
Add 8 to both sides:
And we have our equation.
Notice that this is a direct variation or proportional equation as we don’t have a y-intercept.