Question

1. $y = x + 3$ and $y = -2x + 3$

solution:

Explanation:

Step1: Find intersection algebraically

Set $x + 3 = -2x + 3$
$\implies x + 2x = 3 - 3$
$\implies 3x = 0$
$\implies x = 0$
Substitute $x=0$ into $y=x+3$: $y=0+3=3$
Intersection point: $(0, 3)$

Step2: Identify intercepts for $y=x+3$

y-intercept: when $x=0$, $y=3$ (point $(0,3)$)
x-intercept: when $y=0$, $0=x+3 \implies x=-3$ (point $(-3,0)$)

Step3: Identify intercepts for $y=-2x+3$

y-intercept: when $x=0$, $y=3$ (point $(0,3)$)
x-intercept: when $y=0$, $0=-2x+3 \implies x=\frac{3}{2}=1.5$ (point $(1.5,0)$)

Step4: Plot lines on grid

1. For $y=x+3$: connect $(-3,0)$ and $(0,3)$, extend the line.
2. For $y=-2x+3$: connect $(1.5,0)$ and $(0,3)$, extend the line.

Answer:

The two lines intersect at the point $(0, 3)$. To graph:

• Plot $y=x+3$ using points $(-3, 0)$ and $(0, 3)$
• Plot $y=-2x+3$ using points $(1.5, 0)$ and $(0, 3)$