SOLUTION: What is the equation for a line that contains the points (0,4) and is parallel to y=2x+3?

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: What is the equation for a line that contains the points (0,4) and is parallel to y=2x+3?      Log On


   

Question 226304: What is the equation for a line that contains the points (0,4) and is parallel to y=2x+3?
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
What is the equation for a line that contains the points (0,4) and is parallel to y=2x+3?

Step 1. We can find the slope by recognizing that parallel lines have the same slope. Since y=2x%2B3 is in slope-intercept form given as y=mx+b where the slope m=2 and the y-intercept b=3 when x=0 or at point (0,b) or (0,3).

Step 2. Now we have to find the line with slope m=2 going through point (0,4).

But the point (0,4) is the y-intercept. Then y=2x+4.

The next sequence of steps will show the same equation but this method is applicable even when the point is not the y-intercept.

Step 3. Given two points (x1,y1) and (x2,y2), then the slope m is given as

m=%28y2-y1%29%2F%28x2-x1%29

Step 4. Let (x1,y1)=(0,4) or x1=2 and y1=0. Let other point be (x2,y2)=(x,y) or x2=x and y2=y.

Step 5. Now we're given m=2. Substituting above values and variables in the slope equation m yields the following steps:

m=%28y2-y1%29%2F%28x2-x1%29

2=%28y-4%29%2F%28x-0%29=%28y-4%29%2Fx

Step 6. Multiply x to both sides to get rid of denominator on right side of equation.

2x=x%2A%28y-4%29%2Fx

2x=y-4 and after adding 4 to both sides yields y=2x%2B4 same result as before.

Step 7. ANSWER: The equation in slope-intercept form is y=2x%2B4


Note: the above equation can be rewritten as

-2x%2By=4

And the graph is shown below which is consistent with the above steps.

Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation -2+x+%2B+1+y+=+4 describes a sloping line. For any
equation ax+by+c = 0, slope is -a%2Fb+=+--2%2F1.
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 4/-2 = -2.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 4/1 = 4.
  • Slope is --2/1 = 2.
  • Equation in slope-intercept form: y=2*x+4.
graph%28+500%2C+500%2C+-2-8%2C+-2%2B8%2C+4-8%2C+4%2B8%2C+2%2Ax%2B4+%29+



I hope the above steps and explanation were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV