SOLUTION: Find an equation of the line passing through the point (5,4) and parallel to the line whose equation is 2x + y = 3.

Algebra ->  Linear-equations -> SOLUTION: Find an equation of the line passing through the point (5,4) and parallel to the line whose equation is 2x + y = 3.      Log On


   

Question 252628: Find an equation of the line passing through the point (5,4) and parallel to the line whose equation
is 2x + y = 3.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

2x%2By=3 Start with the given equation.


y=3-2x Subtract 2x from both sides.


y=-2x%2B3 Rearrange the terms.


We can see that the equation y=-2%2Ax%2B3 has a slope m=-2 and a y-intercept b=3.


Since parallel lines have equal slopes, this means that we know that the slope of the unknown parallel line is m=-2.
Now let's use the point slope formula to find the equation of the parallel line by plugging in the slope m=-2 and the coordinates of the given point .


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y-4=-2%28x-5%29 Plug in m=-2, x%5B1%5D=5, and y%5B1%5D=4


y-4=-2x%2B-2%28-5%29 Distribute


y-4=-2x%2B10 Multiply


y=-2x%2B10%2B4 Add 4 to both sides.


y=-2x%2B14 Combine like terms.


So the equation of the line parallel to 2x%2By=3 that goes through the point is y=-2x%2B14.


Here's a graph to visually verify our answer:


Graph of the original equation y=-2%2Ax%2B3 (red) and the parallel line y=-2x%2B14 (green) through the point .