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Question 785318: Find a linear equation whose graph is the straight line with the given properties.
Through
(23, −5.1)
and increasing at a rate of 15 units of y per unit of x.
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website! If the value of  changes by  units when the value of  changes by  ,
then the slope of that line is 
and if line goes through ( , ), then equation will be:
| Solved by pluggable solver: FIND a line by slope and one point |
What we know about the line whose equation we are trying to find out:
- it goes through point (23, -5.1)
- it has a slope of 15
First, let's draw a diagram of the coordinate system with point (23, -5.1) 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=15, 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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since you cannot see a line on a graph above, here is another graph:
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