SOLUTION: Please write an equation (a) in slope-intercept form and (b) in standard form for the line passing through (-3,6) and parallel to x+2y=5.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Please write an equation (a) in slope-intercept form and (b) in standard form for the line passing through (-3,6) and parallel to x+2y=5.      Log On


   

Question 978000: Please write an equation (a) in slope-intercept form and (b) in standard form for the line passing through (-3,6) and parallel to x+2y=5.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

the line passing through (-3,6) and parallel to x%2B2y=5
in slope-intercept form:
2y=-x%2B5
y=-x%2F2%2B5%2F2
y=-%281%2F2%29x%2B5%2F2

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%2F2 (its from the slope of y=%281%2F2%29%2Ax%2B5%2F2 which is also 1%2F2). Also since the unknown line goes through (-3,6), 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-6=%281%2F2%29%2A%28x%2B3%29 Plug in m=1%2F2, x%5B1%5D=-3, and y%5B1%5D=6



y-6=%281%2F2%29%2Ax-%281%2F2%29%28-3%29 Distribute 1%2F2



y-6=%281%2F2%29%2Ax%2B3%2F2 Multiply



y=%281%2F2%29%2Ax%2B3%2F2%2B6Add 6 to both sides to isolate y

y=%281%2F2%29%2Ax%2B3%2F2%2B12%2F2 Make into equivalent fractions with equal denominators



y=%281%2F2%29%2Ax%2B15%2F2 Combine the fractions



y=%281%2F2%29%2Ax%2B15%2F2 Reduce any fractions

So the equation of the line that is parallel to y=%281%2F2%29%2Ax%2B5%2F2 and goes through (-3,6) is y=%281%2F2%29%2Ax%2B15%2F2


So here are the graphs of the equations y=%281%2F2%29%2Ax%2B5%2F2 and y=%281%2F2%29%2Ax%2B15%2F2



graph of the given equation y=%281%2F2%29%2Ax%2B5%2F2 (red) and graph of the line y=%281%2F2%29%2Ax%2B15%2F2(green) that is parallel to the given graph and goes through (-3,6)