To find the slope and the [tex]$y$[/tex]-intercept of the given equation [tex]\( y - 3(x - 1) = 0 \)[/tex], we need to rearrange it into the slope-intercept form, which is [tex]\( y = mx + b \)[/tex]. Here, [tex]\( m \)[/tex] represents the slope and [tex]\( b \)[/tex] represents the [tex]$y$[/tex]-intercept.
1. Start with the given equation:
[tex]\[ y - 3(x - 1) = 0 \][/tex]
2. Distribute the 3 inside the parentheses:
[tex]\[ y - 3x + 3 = 0 \][/tex]
3. Isolate [tex]\( y \)[/tex] by adding [tex]\( 3x \)[/tex] and subtracting 3 from both sides:
[tex]\[ y = 3x - 3 \][/tex]
Now, the equation is in the slope-intercept form [tex]\( y = mx + b \)[/tex].
- The slope [tex]\( m \)[/tex] is the coefficient of [tex]\( x \)[/tex], which is [tex]\( 3 \)[/tex].
- The [tex]$y$[/tex]-intercept [tex]\( b \)[/tex] is the constant term, which is [tex]\( -3 \)[/tex].
Thus, the correct answer is:
D. Slope [tex]\( = 3 \)[/tex] and [tex]$y$[/tex]-intercept [tex]\( = -3 \)[/tex]
