Question

graph these equations:
$y = x - 3$
$y = -x + 5$
click to select points on the graph.

Explanation:

Step1: Find intercepts for $y=x-3$

For x-intercept: set $y=0$, $0=x-3 \implies x=3$, so point $(3,0)$.
For y-intercept: set $x=0$, $y=0-3=-3$, so point $(0,-3)$.

Step2: Find intercepts for $y=-x+5$

For x-intercept: set $y=0$, $0=-x+5 \implies x=5$, so point $(5,0)$.
For y-intercept: set $x=0$, $y=0+5=5$, so point $(0,5)$.

Step3: Locate intersection point

Solve $x-3=-x+5$:
$x+x=5+3$
$2x=8 \implies x=4$
Substitute $x=4$ into $y=x-3$: $y=4-3=1$, so point $(4,1)$.

Step4: Plot and connect points

For $y=x-3$: draw a line through $(3,0)$ and $(0,-3)$.
For $y=-x+5$: draw a line through $(5,0)$ and $(0,5)$. Both lines cross at $(4,1)$.

Answer:

1. For $y = x - 3$: Plot points $(0, -3)$ and $(3, 0)$, then draw a straight line through them.
2. For $y = -x + 5$: Plot points $(0, 5)$ and $(5, 0)$, then draw a straight line through them.
3. The two lines intersect at the point $(4, 1)$.