SOLUTION: Write the slope-intercept for of the equation of a line passing through the point (-2,3) and parallel to the line equation 2x-2y=8.

Algebra ->  Linear-equations -> SOLUTION: Write the slope-intercept for of the equation of a line passing through the point (-2,3) and parallel to the line equation 2x-2y=8.      Log On


   

Question 99557: Write the slope-intercept for of the equation of a line passing through the point (-2,3) and parallel to the line equation 2x-2y=8.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!



First convert the standard equation 2x-2y=8 into slope intercept form

Solved by pluggable solver: Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa)
Convert from standard form (Ax+By = C) to slope-intercept form (y = mx+b)


2x-2y=8 Start with the given equation


2x-2y-2x=8-2x Subtract 2x from both sides


-2y=-2x%2B8 Simplify


%28-2y%29%2F%28-2%29=%28-2x%2B8%29%2F%28-2%29 Divide both sides by -2 to isolate y


y+=+%28-2x%29%2F%28-2%29%2B%288%29%2F%28-2%29 Break up the fraction on the right hand side


y+=+1x-4 Reduce and simplify


The original equation 2x-2y=8 (standard form) is equivalent to y+=+1x-4 (slope-intercept form)


The equation y+=+1x-4 is in the form y=mx%2Bb where m=1 is the slope and b=-4 is the y intercept.








Now let's find the equation of the line that is parallel to y=1x-4 which goes through (-2,3)

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 (its from the slope of y=1%2Ax-4 which is also 1). Also since the unknown line goes through (-2,3), 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-3=1%2A%28x%2B2%29 Plug in m=1, x%5B1%5D=-2, and y%5B1%5D=3



y-3=1%2Ax-%281%29%28-2%29 Distribute 1



y-3=1%2Ax%2B2 Multiply



y=1%2Ax%2B2%2B3Add 3 to both sides to isolate y

y=1%2Ax%2B5 Combine like terms

So the equation of the line that is parallel to y=1%2Ax-4 and goes through (-2,3) is y=1%2Ax%2B5


So here are the graphs of the equations y=1%2Ax-4 and y=1%2Ax%2B5



graph of the given equation y=1%2Ax-4 (red) and graph of the line y=1%2Ax%2B5(green) that is parallel to the given graph and goes through (-2,3)