Equation of a line in point-slope form
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A line passes through the points $(-3, 4)$ and $(1, 12)$. What is an equation of the line in point-slope form?
A) $y - 4 = 2(x - 3)$
B) $y - 4 = -2(x + 3)$
C) $y - 4 = 2(x + 3)$
D) $y - 4 = rac{1}{2}(x - 3)$
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Hello! We are asked to find the point slope form equation of a line that passes through the points negative three, four and one, twelve. Let's start by identifying our given information.
Finding Point-Slope Form
Points: $(-3, 4)$ and $(1, 12)$
Recall that the point slope form of a linear equation is written as y minus y one equals m times the quantity x minus x one.
In this formula, m represents the slope of the line. Before we can write the equation, we need to calculate this slope using the formula m equals y two minus y one over x two minus x one.
Let's plug in our values. Taking negative three, four as our first point and one, twelve as our second, we get twelve minus four in the numerator.
In the denominator, we have one minus negative three.
Twelve minus four is eight, and one minus negative three is the same as one plus three, which is four.
Eight divided by four simplifies to two. So the slope of our line is two.
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