algebra

[4reading]

I am trying to help my daughter with her algebra homework. Chapter is "systems of Equations"

Problem: Solve by graphing
x=-y
x+y=4

We can't find the point they intersect. Not really sure how to find the slope of x=-y

 

[Mrspi]

I am trying to help my daughter with her algebra homework. Chapter is "systems of Equations"

Problem: Solve by graphing
x=-y
x+y=4

We can't find the point they intersect. Not really sure how to find the slope of x=-y

If you solve each equation for y, the slope should be easy to find. "slope-intercept" form for an equation is y = mx + b In that form, "m" is the slope, and "b" is the y-intercept.

Your first equation is

x = -y

If you multiply both sides of that equation by -1, you'll get "y" on one side:
-1(x) = -1(-y)
-x = y
or,
y = -x

We could write that as
y = -x + 0

Do you see that the slope is -1? And that the y-intercept (the point where the line crosses the y-axis) is 0?

Your second equation is

x + y = 4
Add -x to both sides:

x + y + -x = 4 + (-x)
y = -x + 4

Do you see that the slope of this line is -1 also? The y-intercept is 4.

If two lines have the same slope, the lines are PARALLEL. Parallel lines do not intersect, so it's no wonder you can't find the point of intersection....there ISN'T one.

 

[4reading]

Thank you!! We were actually doing it correctly. My daughter thought that there had to be a point where they intersected which lead our struggle. Many thanks again!