SOLUTION: Write the point-slope form of the equation of the line described. through: (2, -5), parallel to y = - 5/2x + 2

Algebra ->  Linear-equations -> SOLUTION: Write the point-slope form of the equation of the line described. through: (2, -5), parallel to y = - 5/2x + 2      Log On


   

Question 995754: Write the point-slope form of the equation of the line described.

through: (2, -5), parallel to y = - 5/2x + 2
Found 2 solutions by MathLover1, solver91311:
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 -5%2F2 (its from the slope of y=%28-5%2F2%29%2Ax%2B2 which is also -5%2F2). Also since the unknown line goes through (2,-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=%28-5%2F2%29%2A%28x-2%29 Plug in m=-5%2F2, x%5B1%5D=2, and y%5B1%5D=-5



y%2B5=%28-5%2F2%29%2Ax%2B%285%2F2%29%282%29 Distribute -5%2F2



y%2B5=%28-5%2F2%29%2Ax%2B10%2F2 Multiply



y=%28-5%2F2%29%2Ax%2B10%2F2-5Subtract -5 from both sides to isolate y

y=%28-5%2F2%29%2Ax%2B10%2F2-10%2F2 Make into equivalent fractions with equal denominators



y=%28-5%2F2%29%2Ax%2B0%2F2 Combine the fractions



y=%28-5%2F2%29%2Ax%2B0 Reduce any fractions

So the equation of the line that is parallel to y=%28-5%2F2%29%2Ax%2B2 and goes through (2,-5) is y=%28-5%2F2%29%2Ax%2B0


So here are the graphs of the equations y=%28-5%2F2%29%2Ax%2B2 and y=%28-5%2F2%29%2Ax%2B0



graph of the given equation y=%28-5%2F2%29%2Ax%2B2 (red) and graph of the line y=%28-5%2F2%29%2Ax%2B0(green) that is parallel to the given graph and goes through (2,-5)

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


The equation of the given line is written in slope-intercept form. Hence, you can determine the slope by inspection. Parallel lines have identical slopes. Use the Point-Slope form:



where are the coordinates of the given point and is the given slope.

John

My calculator said it, I believe it, that settles it