What we know about the line whose equation we are trying to find out:
- it goes through point (4, -2)
- it has a slope of -1
First, let's draw a diagram of the coordinate system with point (4, -2) plotted with a little blue dot:
Write this down: the formula for the equation, given point and intercept a, is
(see a paragraph below explaining why this formula is correct)
Given that a=-1, and , we have the equation of the line:
Explanation: Why did we use formula ? Explanation goes here. We are trying to find equation y=ax+b. The value of slope (a) is already given to us. We need to find b. If a point (, ) lies on the line, it means that it satisfies the equation of the line. So, our equation holds for (, ): Here, we know a, , and , and do not know b. It is easy to find out: . So, then, the equation of the line is: .
Here's the graph:
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