Question

1. $y - 2 = 4(x - 1)$

Explanation:

Step1: Rewrite to slope-intercept form

Expand and isolate $y$:

$$\begin{align*} y - 2 &= 4(x - 1)\\ y - 2 &= 4x - 4\\ y &= 4x - 4 + 2\\ y &= 4x - 2 \end{align*}$$

Step2: Identify key points

1. Y-intercept: When $x=0$, $y=4(0)-2=-2$, so the point is $(0, -2)$.
2. Another point: When $x=1$, $y=4(1)-2=2$, so the point is $(1, 2)$.

Step3: Plot and draw the line

Plot $(0, -2)$ and $(1, 2)$, then draw a straight line through them (extending in both directions, using the slope $m=4$ to find additional points if needed: for every 1 unit right, move 4 units up).

Answer:

The line $y=4x-2$ (rewritten from $y-2=4(x-1)$) is graphed by plotting points $(0, -2)$ and $(1, 2)$ and drawing a straight line through them, extending across the coordinate plane.