Question 1074031: -x+y=3
4x+4y=9
Find if these are parallel, perpendicular or neither.
Is this neither and is this where you substitute 0 for x and y?
Can someone show me the steps so I can understand? Thanks 😊
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! If two lines are parallel, they have the same slope,
and if two lines have the same slope, they are parallel.
If two lines are perpendicular, the product of their slopes is  ,
and if the product of the slopes of two lines is , the lines are perpendicular.
If you solve for y in a linear equation,
you get the equation in the slope-intercept form,
and in that form, the coefficient of the x is the slope.
For example, solving for y in  ,
you get  .
The invisible  that is multiplying x is the slope,
and the 3 is the y-intercept (or intercept for short).
That is the y-coordinate of the point where the line crosses the y-axis.
You do not need to solve for y, if all you need is the slope;
just dividing the coefficients of x and y, and changing the sign is enough.
For example, if you were to solve
 for y, the first step would be
 , turning the 4x on the same side as the 4y into -4x on the other side.
That changed the sign of the b4 that was the coefficient of x.
The next step would be dividing everything by the 4 multiplying the y,
and that would leave  (the slope) as coefficient of x.
Now you know that the slopes of those two lines are and .
Since their product is  ,
the lines are perpendicular.
|
|
|
