SOLUTION: What is the equation of a line that is parallel to y=4x -3 and goes through the point (0,10)

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Question 962889: What is the equation of a line that is parallel to y=4x -3 and goes through the point (0,10)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line


Since any two parallel lines have the same slope we know the slope of the unknown line is 4 (its from the slope of y=4%2Ax-3 which is also 4). Also since the unknown line goes through (0,10), we can find the equation by plugging in this info into the point-slope formula

Point-Slope Formula:

y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope and (x%5B1%5D,y%5B1%5D) is the given point



y-10=4%2A%28x-0%29 Plug in m=4, x%5B1%5D=0, and y%5B1%5D=10



y-10=4%2Ax-%284%29%280%29 Distribute 4



y-10=4%2Ax-0 Multiply



y=4%2Ax-0%2B10Add 10 to both sides to isolate y

y=4%2Ax%2B10 Combine like terms

So the equation of the line that is parallel to y=4%2Ax-3 and goes through (0,10) is y=4%2Ax%2B10


So here are the graphs of the equations y=4%2Ax-3 and y=4%2Ax%2B10



graph of the given equation y=4%2Ax-3 (red) and graph of the line y=4%2Ax%2B10(green) that is parallel to the given graph and goes through (0,10)