SOLUTION: Find the equation of each line. Write the answer in slope-intercept form. The line is parallel to -3x + 2y = 9 and contains the point (-2,1).

Algebra ->  Graphs -> SOLUTION: Find the equation of each line. Write the answer in slope-intercept form. The line is parallel to -3x + 2y = 9 and contains the point (-2,1).       Log On


   

Question 91189: Find the equation of each line. Write the answer in slope-intercept form.
The line is parallel to -3x + 2y = 9 and contains the point (-2,1).
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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)


-3x%2B2y=9 Start with the given equation


-3x%2B2y%2B3x=9%2B3x Add 3x to both sides


2y=3x%2B9 Simplify


%282y%29%2F%282%29=%283x%2B9%29%2F%282%29 Divide both sides by 2 to isolate y


y+=+%283x%29%2F%282%29%2B%289%29%2F%282%29 Break up the fraction on the right hand side


y+=+%283%2F2%29x%2B9%2F2 Reduce and simplify


The original equation -3x%2B2y=9 (standard form) is equivalent to y+=+%283%2F2%29x%2B9%2F2 (slope-intercept form)


The equation y+=+%283%2F2%29x%2B9%2F2 is in the form y=mx%2Bb where m=3%2F2 is the slope and b=9%2F2 is the y intercept.





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 3%2F2 (its from the slope of y=%283%2F2%29%2Ax%2B9%2F2 which is also 3%2F2). Also since the unknown line goes through (-2,1), 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-1=%283%2F2%29%2A%28x%2B2%29 Plug in m=3%2F2, x%5B1%5D=-2, and y%5B1%5D=1



y-1=%283%2F2%29%2Ax-%283%2F2%29%28-2%29 Distribute 3%2F2



y-1=%283%2F2%29%2Ax%2B6%2F2 Multiply



y=%283%2F2%29%2Ax%2B6%2F2%2B1Add 1 to both sides to isolate y

y=%283%2F2%29%2Ax%2B6%2F2%2B2%2F2 Make into equivalent fractions with equal denominators



y=%283%2F2%29%2Ax%2B8%2F2 Combine the fractions



y=%283%2F2%29%2Ax%2B4 Reduce any fractions

So the equation of the line that is parallel to y=%283%2F2%29%2Ax%2B9%2F2 and goes through (-2,1) is y=%283%2F2%29%2Ax%2B4


So here are the graphs of the equations y=%283%2F2%29%2Ax%2B9%2F2 and y=%283%2F2%29%2Ax%2B4



graph of the given equation y=%283%2F2%29%2Ax%2B9%2F2 (red) and graph of the line y=%283%2F2%29%2Ax%2B4(green) that is parallel to the given graph and goes through (-2,1)