Draw the graphs for the linear equations y = -x + 4 and y = -x - 4. What is their relationship?

The first equation is $y = -x + 4$.
To find the y-intercept, set $x = 0$:

$$y = -(0) + 4 = 4$$

So, the y-intercept is $(0, 4)$.
To find the x-intercept, set $y = 0$:

$$0 = -x + 4$$ $$x = 4$$

So, the x-intercept is $(4, 0)$.

The second equation is $y = -x - 4$.
To find the y-intercept, set $x = 0$:

$$y = -(0) - 4 = -4$$

So, the y-intercept is $(0, -4)$.
To find the x-intercept, set $y = 0$:

$$0 = -x - 4$$ $$x = -4$$

So, the x-intercept is $(-4, 0)$.

• For the first line, $y = -x + 4$: Plot the points $(0, 4)$ and $(4, 0)$ on a coordinate plane. Draw a straight line passing through these two points. This line has a slope of $-1$ and a y-intercept of 4.
• For the second line, $y = -x - 4$: Plot the points $(0, -4)$ and $(-4, 0)$ on the same coordinate plane. Draw a straight line passing through these two points. This line also has a slope of $-1$ and a y-intercept of $-4$.

Both lines are parallel because they have the same slope ($m = -1$).