How do you graph the lines y = x + 1 and y − x = 2 on a Cartesian plane?

• When $x = 0$:

So, one point is $(0, 1)$.

• When $x = 2$:

So, another point is $(2, 3)$.

For the second line: $y - x = 2$
Rearrange this equation into the slope-intercept form $y = mx + c$:

Here, the slope $m = 1$ and the y-intercept $c = 2$.

• When $x = 0$:

So, one point is $(0, 2)$.

• When $x = 2$:

So, another point is $(2, 4)$.

Draw an x-axis (horizontal) and a y-axis (vertical) intersecting at the origin $(0,0)$. Label the axes.

• For $y = x + 1$: Plot $(0, 1)$ and $(2, 3)$. Draw a straight line through these points and label it $y = x + 1$.
• For $y = x + 2$: Plot $(0, 2)$ and $(2, 4)$. Draw a straight line through these points and label it $y = x + 2$.

Note that both lines have the same slope ($m=1$), which means they are parallel to each other.