write the equation in slope-intercept form of the line that has a slope of 2 and contains the point (3,7)
1 answer:
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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.
Answer:
Composition:
Domain = { }
Step-by-step explanation:
Given
The requested composition becomes:
Then the Domain consists of all Real x-values for which the function is defined. In this case, the function is defined for all x-values for which the square root is defined, that is all x values for which:
(so the square root is defined in the Real number system)
This means
The Domain is then all the Real x-values such that