SOLUTION: Find the equation of the line in point slope form that passes through (4,3)and is parallel to the line 3x-y=7.

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Question 153218: Find the equation of the line in point slope form that passes through (4,3)and is parallel to the line 3x-y=7.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

3x-y=7 Start with the given equation.


-y=7-3x Subtract 3x from both sides.


-y=-3x%2B7 Rearrange the terms.


y=%28-3x%2B7%29%2F%28-1%29 Divide both sides by -1 to isolate y.


y=%28%28-3%29%2F%28-1%29%29x%2B%287%29%2F%28-1%29 Break up the fraction.


y=3x-7 Reduce.


We can see that the equation y=3x-7 has a slope m=3 and a y-intercept b=-7.


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


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


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


y-3=3x%2B3%28-4%29 Distribute


y-3=3x-12 Multiply


y=3x-12%2B3 Add 3 to both sides.


y=3x-9 Combine like terms.


So the equation of the line parallel to 3x-y=7 that goes through the point is y=3x-9.


Here's a graph to visually verify our answer:
Graph of the original equation y=3%2Ax-7 (red) and the parallel line y=3x-9 (green) through the point .