SOLUTION: state the equation (in point-slope form)of the line that passes through (-10,8) and is parallel to the line 5x+2y=10

Algebra ->  Linear-equations -> SOLUTION: state the equation (in point-slope form)of the line that passes through (-10,8) and is parallel to the line 5x+2y=10      Log On


   

Question 227556: state the equation (in point-slope form)of the line that passes through (-10,8) and is parallel to the line 5x+2y=10
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

5x%2B2y=10 Start with the given equation.


2y=10-5x Subtract 5x from both sides.


2y=-5x%2B10 Rearrange the terms.


y=%28-5x%2B10%29%2F%282%29 Divide both sides by 2 to isolate y.


y=%28%28-5%29%2F%282%29%29x%2B%2810%29%2F%282%29 Break up the fraction.


y=-%285%2F2%29x%2B5 Reduce.


We can see that the equation y=-%285%2F2%29x%2B5 has a slope m=-5%2F2 and a y-intercept b=5.


Since parallel lines have equal slopes, this means that we know that the slope of the unknown parallel line is m=-5%2F2.
Now let's use the point slope formula to find the equation of the parallel line by plugging in the slope m=-5%2F2 and the coordinates of the given point .


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


y-8=%28-5%2F2%29%28x--10%29 Plug in m=-5%2F2, x%5B1%5D=-10, and y%5B1%5D=8


y-8=%28-5%2F2%29%28x%2B10%29 Rewrite x--10 as x%2B10


y-8=%28-5%2F2%29x%2B%28-5%2F2%29%2810%29 Distribute


y-8=%28-5%2F2%29x-25 Multiply


y=%28-5%2F2%29x-25%2B8 Add 8 to both sides.


y=%28-5%2F2%29x-17 Combine like terms.


So the equation of the line parallel to 5x%2B2y=10 that goes through the point is y=%28-5%2F2%29x-17.


Here's a graph to visually verify our answer:
Graph of the original equation y=-%285%2F2%29x%2B5 (red) and the parallel line y=%28-5%2F2%29x-17 (green) through the point .