SOLUTION: Write the equation of the line L satisfying the given geometric conditions: L has y - intercept (0,3) and is parallel to the line with equation y= 3x-5

Algebra ->  Graphs -> SOLUTION: Write the equation of the line L satisfying the given geometric conditions: L has y - intercept (0,3) and is parallel to the line with equation y= 3x-5      Log On


   

Question 104555: Write the equation of the line L satisfying the given geometric conditions:
L has y - intercept (0,3) and is parallel to the line with equation y= 3x-5
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
y=mx+b where m=slope
y=3x-5
m=3; (0,3)
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 (0, 3)

  • it has a slope of 3



First, let's draw a diagram of the coordinate system with point (0, 3) plotted with a little blue dot:



Write this down: the formula for the equation, given point x%5B1%5D%2C+y%5B1%5D and intercept a, is

y=ax+%2B+%28y%5B1%5D-a%2Ax%5B1%5D%29 (see a paragraph below explaining why this formula is correct)

Given that a=3, and system%28+x%5B1%5D+=+0%2C+y%5B1%5D+=+3+%29+, we have the equation of the line:

y=3%2Ax+%2B+3

Explanation: Why did we use formula y=ax+%2B+%28y%5B1%5D+-+a%2Ax%5B1%5D%29 ? 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 (x%5B1%5D, y%5B1%5D) lies on the line, it means that it satisfies the equation of the line. So, our equation holds for (x%5B1%5D, y%5B1%5D): y%5B1%5D+=+a%2Ax%5B1%5D%2Bb Here, we know a, x%5B1%5D, and y%5B1%5D, and do not know b. It is easy to find out: b=y%5B1%5D-a%2Ax%5B1%5D. So, then, the equation of the line is: +y=ax%2B%28y%5B1%5D-a%2Ax%5B1%5D%29+.

Here's the graph: