SOLUTION: find the equation of the line that contains the point (-1,-5) and is parallel to the line 7x-4y=1.

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Question 661691: find the equation of the line that contains the point (-1,-5) and is parallel to the line 7x-4y=1.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
given:
the point (-1,-5) and is parallel to the line 7x-4y=1
first, write 7x-4y=1 in slope-intercept form
7x-1=4y

y=%287%2F4%29x-1%2F4

solution:

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 1.75 (its from the slope of y=1.75%2Ax-0.25 which is also 1.75). Also since the unknown line goes through (-1,-5), 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%2B5=1.75%2A%28x%2B1%29 Plug in m=1.75, x%5B1%5D=-1, and y%5B1%5D=-5



y%2B5=1.75%2Ax-%281.75%29%28-1%29 Distribute 1.75



y%2B5=1.75%2Ax%2B1.75 Multiply



y=1.75%2Ax%2B1.75-5Subtract -5 from both sides to isolate y

y=1.75%2Ax-3.25 Combine like terms

So the equation of the line that is parallel to y=1.75%2Ax-0.25 and goes through (-1,-5) is y=1.75%2Ax-3.25


So here are the graphs of the equations y=1.75%2Ax-0.25 and y=1.75%2Ax-3.25



graph of the given equation y=1.75%2Ax-0.25 (red) and graph of the line y=1.75%2Ax-3.25(green) that is parallel to the given graph and goes through (-1,-5)