The classic 60° triangle has a hypotenuse of length 2, an opposite side of length √3 and an adjacent side of length 1....find th
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Answer:
Part A)
The slope is 3.
Part B)
Part C)
Step-by-step explanation:
We know that the line goes through the points (-3, 1) and (-2, 4).
Part A)
To find the slope of a line given two points, we can use the slope formula:
Where (x₁, y₁) and (x₂, y₂) are our two points.
So, let’s let (-3, 1) be (x₁, y₁) and let (-2, 4) be (x₂, y₂). Substitute appropriately:
Evaluate:
Hence, the slope of our line is 3.
Part B)
Point-slope form is given by:
Where m is our slope and (x₁, y₁) is a point.
So, let’s substitute 3 for m.
For our point, we can use either of the two given. Let’s use (-3, 1) for consistency. So, let (-3, 1) be (x₁, y₁). Therefore:
Simplify. Hence, our point-slope form is:
Part C)
To rewrite into slope-intercept form, we can just solve for y from our point-slope form. So, we have:
Distribute on the right:
Add 1 to boths sides. So, our slope-intercept equation is: