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Find the slope and the [tex]\(y\)[/tex]-intercept of the equation [tex]\(y - 3(x - 1) = 0\)[/tex].

A. slope [tex]\(=-3\)[/tex] and [tex]\(y\)[/tex]-intercept [tex]\(=-3\)[/tex]

B. slope [tex]\(=3\)[/tex] and [tex]\(y\)[/tex]-intercept [tex]\(=3\)[/tex]

C. slope [tex]\(=-3\)[/tex] and [tex]\(y\)[/tex]-intercept [tex]\(=3\)[/tex]

D. slope [tex]\(=3\)[/tex] and [tex]\(y\)[/tex]-intercept [tex]\(=-3\)[/tex]


Sagot :

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].