To find the slope and the [tex]\( y \)[/tex]-intercept of the equation [tex]\( y - 3(x - 1) = 0 \)[/tex], we need to rearrange the equation into the slope-intercept form, which is [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] represents the slope and [tex]\( b \)[/tex] represents the [tex]\( y \)[/tex]-intercept. Let's do this step-by-step:
1. Start with the given equation:
[tex]\[
y - 3(x - 1) = 0
\][/tex]
2. Distribute the 3 on the right-hand side:
[tex]\[
y - 3x + 3 = 0
\][/tex]
3. Move the constant term to the other side of the equation to isolate [tex]\( y \)[/tex]:
[tex]\[
y = 3x - 3
\][/tex]
Now, we can clearly identify the slope and the [tex]\( y \)[/tex]-intercept from the slope-intercept form [tex]\( y = mx + b \)[/tex]:
- The slope [tex]\( m \)[/tex] is the coefficient of [tex]\( x \)[/tex], which is 3.
- The [tex]\( y \)[/tex]-intercept [tex]\( b \)[/tex] is the constant term, which is -3.
Hence, the slope is 3 and the [tex]\( y \)[/tex]-intercept is -3.
The correct answer is:
D. slope [tex]\( = 3 \)[/tex] and [tex]\( y \)[/tex]-intercept [tex]\( = -3 \)[/tex].
