SOLUTION: I have two questions, having to write an equation in standard form for each line described: 29) The line that passes through the point (-1,3) and is parallel to the graph of 3x-

Algebra ->  Graphs -> SOLUTION: I have two questions, having to write an equation in standard form for each line described: 29) The line that passes through the point (-1,3) and is parallel to the graph of 3x-      Log On


   

Question 128034This question is from textbook algebra: structure and method: book1
: I have two questions, having to write an equation in standard form for each line described:
29) The line that passes through the point (-1,3) and is parallel to the graph of 3x-y=4.
31) The line that passes through the point (-4,-5) and has the same y-intercept as the graph x+3y=-9.
I PLEASE HELP!!!!!! The answers are 3x-y=-6 and -x+2y=-6, but I don't know how to get there. HELP MUCH APPRECIATED!!!! This question is from textbook algebra: structure and method: book1

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
For the first problem, remember that lines are parallel if and only if their slopes are equal. So the first thing to do is find the slope of the given line by putting the equation into slope-intercept form (y=mx%2Bb, i.e. solve the equation for y.
3x-y=4

Add -3x to both sides:
-y=-3x%2B4

Multiply by -1:
y=3x-4

Now we know that the slope of the given line is 3 because that is the coefficient on the x term.

If you know a point on a line and the slope of the line, you can use the point-slope form of the line to derive the equation.

y-y%5B1%5D=m%28x-x%5B1%5D%29, where m is the slope, x%5B1%5D is the x-coordinate of the given point, and y%5B1%5D is the y-coordinate of the given point.

y-3=3%28x-%28-1%29%29

y-3=3x%2B3

y=3x%2B6 is the slope-intercept form of the required equation, or 3x-y=-6 is the standard form Ax%2BBy=C.

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For the second problem, you are given two points, one of them directly, and the other indirectly by knowing the y-intercept. The given equation is x%2B3y=-9 and this needs to be put into slope-intercept form by solving for y:

x%2B3y=-9

3y=-x-9

y=%28-x%2F3%29-3.

Now we know that the y-intercept of the given line is -3. The y-intercept is the point where the line intersects the y-axis. We know that the x-coordinate of all points on the y-axis is 0, so the ordered pair that we need is (0,-3).

Next we need the two-point form of the line to derive the desired equation:
y-y%5B1%5D=%28%28y%5B1%5D-y%5B2%5D%29%2F%28x%5B1%5D-x%5B2%5D%29%29%28x-x%5B1%5D%29 and the two points: (0,-3) and (-4,-5)
Substituting the coordinate values:
y-%28-3%29=%28%28-3-%28-5%29%29%2F%280-%28-4%29%29%29%28x-0%29

Now do the arithmetic:
y%2B3=%282%2F4%29%28x%29

4y%2B12=2x

2y%2B6=x

-x%2B2y=-6, is the answer you were looking for, though I would have written:

x-2y=6