Question 114715: Write the equation of the line that passes through point (6,4) with a slope of 2.
Found 2 solutions by MathLover1, TP:
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website!
if the line that passes through point ( , ) with a slope of  ,the equation of the line would 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 (6, 4)
- it has a slope of 2
First, let's draw a diagram of the coordinate system with point (6, 4) 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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Answer by TP(29)  (Show Source):
You can put this solution on YOUR website! The equation of a line can be written as y=mx+c where m=gradient(slope) and c is the y value where the line cuts the vertical y axis.
Your slope is 2 so we have y=2x+c.(i)
Now we need to find the value of c.
In ANY question you must use all the info given(although with some vindictive posers of questions you may get 'red herrings').
Here we are told that the line passes through (6,4) and so replacing x and y by 6 and 4 respectively in (i)we get:
4=2*6+c=12+c.
Hence c=-8.
Your equation then is y=2x-8ANS
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