Question 82957: Can someone please, please show me how to do this?
Write the equation of the line which passes through the point (2, 1) and is parallel to the line with equation y=5/2 x+6
Found 2 solutions by jim_thompson5910, checkley75:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Since the unknown line is parallel to  we know the slope of this line (of both lines actually) is  . So we know the slope is and the line goes through (2,1), so lets find the equation:
| 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 (2, 1)
- it has a slope of 2.5
First, let's draw a diagram of the coordinate system with point (2, 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=2.5, 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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or in other words, the equation is
Answer by checkley75(3666) (Show Source):
You can put this solution on YOUR website! ANY PARALLEL LINE TO Y=5/2X+6 HAS A SLOPE OF (5/2).
THUS THE LINE PARALLEL TO THIS LINE THROUGH THE POINTS (2,1) IS:
1=5/2*2+b b BEING THE Y INTERCEPT.
1=5+b
b=1-5
b=-4 THE Y IMTERCEPT.
THUS THE EQUATION FOR THIS LINE IS:
Y=5/2X-5 ANSWER.
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