SOLUTION: Write an equation in the slope intercept form if possible: The line goes through the (1,4) and is parallel to 5 + 4y = 3x

Algebra ->  Linear-equations -> SOLUTION: Write an equation in the slope intercept form if possible: The line goes through the (1,4) and is parallel to 5 + 4y = 3x      Log On


   

Question 102642: Write an equation in the slope intercept form if possible: The line goes through the (1,4) and is parallel to 5 + 4y = 3x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First solve for y:

5+%2B+4y+=+3x Start with the given equation


+4y+=+3x-5 Subtract 5 from both sides


+cross%28%281%2F4%29%284%29%29y+=%281%2F4%29%28+3x-5%29 Multiply both sides by 1%2F4 to isolate y



+y+=%281%2F4%293x-%281%2F4%295%29 Distribute


+y+=%283%2F4%293x-5%2F4%29 Multiply. So now the equation is in slope-intercept form y=mx%2Bb where the slope is m=3%2F4 and the y-intercept is b=-5%2F4


Now let's find the equation of the line that is parallel to +y+=%283%2F4%293x-5%2F4%29 and goes through (1,4)


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%2F4 (its from the slope of y=%283%2F4%29%2Ax-5%2F4 which is also 3%2F4). Also since the unknown line goes through (1,4), 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-4=%283%2F4%29%2A%28x-1%29 Plug in m=3%2F4, x%5B1%5D=1, and y%5B1%5D=4



y-4=%283%2F4%29%2Ax-%283%2F4%29%281%29 Distribute 3%2F4



y-4=%283%2F4%29%2Ax-3%2F4 Multiply



y=%283%2F4%29%2Ax-3%2F4%2B4Add 4 to both sides to isolate y

y=%283%2F4%29%2Ax-3%2F4%2B16%2F4 Make into equivalent fractions with equal denominators



y=%283%2F4%29%2Ax%2B13%2F4 Combine the fractions



y=%283%2F4%29%2Ax%2B13%2F4 Reduce any fractions

So the equation of the line that is parallel to y=%283%2F4%29%2Ax-5%2F4 and goes through (1,4) is y=%283%2F4%29%2Ax%2B13%2F4


So here are the graphs of the equations y=%283%2F4%29%2Ax-5%2F4 and y=%283%2F4%29%2Ax%2B13%2F4



graph of the given equation y=%283%2F4%29%2Ax-5%2F4 (red) and graph of the line y=%283%2F4%29%2Ax%2B13%2F4(green) that is parallel to the given graph and goes through (1,4)