Question 520780: find the equation of the line with slope 3 containing the point (2,-5) in both point-slope form and slope-intercept form.
Answer by MathLover1(20849)   (Show Source):
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What we know about the line whose equation we are trying to find out:
- it goes through point (2, -5)
- it has a slope of 3
First, let's draw a diagram of the coordinate system with point (2, -5) 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=3, 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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The other format for straight-line equations is called the "point-slope" form. For this one, they give you a point ( ,  ) and a slope  , and have you plug it into this formula:
so, you will have:
and slope-intercept form is:
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