SOLUTION: write the equation of the line that parallel to f(x)=3x-7 and goes through the point (0,4)

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Question 333866: write the equation of the line that parallel to f(x)=3x-7 and goes through the point (0,4)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: y=3x-7 is the same as f%28x%29=3x-7


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-4=3%28x-0%29 Plug in m=3, x%5B1%5D=0, and y%5B1%5D=4


y-4=3x%2B3%28-0%29 Distribute


y-4=3x%2B0 Multiply


y=3x%2B0%2B4 Add 4 to both sides.


y=3x%2B4 Combine like terms.


So the equation of the line parallel to y=3x-7 that goes through the point is y=3x%2B4.


Here's a graph to visually verify our answer:
Graph of the original equation y=3x-7 (red) and the parallel line y=3x%2B4 (green) through the point .