Question 701278: find the equation of a line that passes through the point (-1,3) and is parallel to the line passing through the points (-2, -3) and (2,5). THANKS
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website! first find the equation of the line passing through the points ( ,  ) and ( , )
| Solved by pluggable solver: FIND EQUATION of straight line given 2 points |
hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (-2, -3) and (x2, y2) = (2, 5).
Slope a is  .
Intercept is found from equation  , or  . From that,
intercept b is  , or  .
y=(2)x + (1)
Your graph:
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since we are looking for the equation of the line that passes through the point ( , ) and is parallel to the line  , we will find it using given point and a slope of which is  because parallel lines have same slope
| 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 (-1, 3)
- it has a slope of 2
First, let's draw a diagram of the coordinate system with point (-1, 3) 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, 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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so, we found that the lines and  are parallel lines, that the line passing through the points (, ) and (,), and the line passing through the point (,)
see it all on a graph:
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