SOLUTION: write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of each equation. (-5,-4),2x+3y=-1

Algebra ->  Graphs -> SOLUTION: write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of each equation. (-5,-4),2x+3y=-1      Log On


   

Question 115946: write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of each equation.
(-5,-4),2x+3y=-1
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
This is a point-slope problem. You are given a point, and enough information to determine the slope, because you are given a parallel line and we know that the slopes of parallel lines are equal.

2x%2B3y=-1 In order to find the slope of a line, solve the equation for y which puts the equation into slope-intercept form y=mx%2Bb where m is the slope and b is the y-intercept.

3y=-2x-1
y=%28%28-2%29%2F3%29x-1%2F3. so now we know that the slope of the line we are trying to define is %28%28-2%29%2F3%29

Knowing a point on the line and the slope, we can now use the point-slope form of the line %28y-y%5B1%5D%29=m%28x-x%5B1%5D%29 to write the equation directly.

y-%28-5%29=%28%28-2%29%2F3%29%28x-%28-4%29%29 is the equation of the specified line, but it needs to be simplified

y%2B5=%28-2%2F3%29%28x%2B4%29

Now, you can put it into standard form ax%2Bby=c:

3y%2B15=-2x-8
2x%2B3y=-23

Or, you could put it into slope-intercept form y=mx%2Bb

y=%28-2%2F3%29x-%2823%2F3%29

Notice that the standard form differs from the given equation only in the constant term. This should give you a clue to the relationship between the coefficients on the x and y terms in a standard form equation and the slope of the line.