SOLUTION: How do I write the slope intercpt form of an equation of the line that passes throught the given point and is parallel to the graph of the equation (4,-6),y=-3/4x+1

Algebra ->  Graphs -> SOLUTION: How do I write the slope intercpt form of an equation of the line that passes throught the given point and is parallel to the graph of the equation (4,-6),y=-3/4x+1      Log On


   

Question 253688: How do I write the slope intercpt form of an equation of the line that passes throught the given point and is parallel to the graph of the equation
(4,-6),y=-3/4x+1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

We can see that the equation y=-%283%2F4%29x%2B1 has a slope m=-3%2F4 and a y-intercept b=1.


Since parallel lines have equal slopes, this means that we know that the slope of the unknown parallel line is m=-3%2F4.
Now let's use the point slope formula to find the equation of the parallel line by plugging in the slope m=-3%2F4 and the coordinates of the given point .


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


y--6=-%283%2F4%29%28x-4%29 Plug in m=-3%2F4, x%5B1%5D=4, and y%5B1%5D=-6


y%2B6=-%283%2F4%29%28x-4%29 Rewrite y--6 as y%2B6


y%2B6=-%283%2F4%29x-%283%2F4%29%28-4%29 Distribute


y%2B6=-%283%2F4%29x%2B3 Multiply


y=-%283%2F4%29x%2B3-6 Subtract 6 from both sides.


y=-%283%2F4%29x-3 Combine like terms.


So the equation of the line parallel to y=-3%2F4x%2B1 that goes through the point is y=-%283%2F4%29x-3.


Here's a graph to visually verify our answer:


Graph of the original equation y=-%283%2F4%29x%2B1 (red) and the parallel line y=-%283%2F4%29x-3 (green) through the point .