Question

intersection.

1. \\( y = 3x - 2 \\) and \\( y = x \\)

solution:

Explanation:

Step1: Set equations equal

Since $y = x$ and $y = 3x - 2$, substitute $y$:
$x = 3x - 2$

Step2: Solve for $x$

Subtract $3x$ from both sides:
$x - 3x = -2$
$-2x = -2$
Divide by $-2$:
$x = \frac{-2}{-2} = 1$

Step3: Find $y$ value

Use $y = x$, so $y = 1$

Answer:

The intersection point is $(1, 1)$

To plot the lines:

• For $y = x$: Plot points like $(-2, -2)$, $(0, 0)$, $(2, 2)$ and draw a straight line through them.
• For $y = 3x - 2$: Use y-intercept $(0, -2)$ and slope 3 (rise 3, run 1) to plot additional points like $(1, 1)$, $(2, 4)$, then draw the line. The lines cross at $(1, 1)$.