Let's start with the given equation:
[tex]\[ 3x - 5y = 12 \][/tex]
We need to convert this 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 y-intercept.
### Step-by-Step Solution:
1. Isolate the [tex]\( y \)[/tex]-term:
Begin by getting [tex]\( -5y \)[/tex] alone on one side of the equation. We can do this by subtracting [tex]\( 3x \)[/tex] from both sides:
[tex]\[ -5y = -3x + 12 \][/tex]
2. Make the coefficient of [tex]\( y \)[/tex] equal to 1:
To isolate [tex]\( y \)[/tex], divide every term by [tex]\(-5\)[/tex]:
[tex]\[ y = \frac{3}{5}x - \frac{12}{5} \][/tex]
This is now in the slope-intercept form [tex]\( y = mx + b \)[/tex], where:
- [tex]\( m \)[/tex] (the slope) is the coefficient of [tex]\( x \)[/tex]
- [tex]\( b \)[/tex] (the y-intercept) is the constant term
### Results:
- The slope ([tex]\( m \)[/tex]) is [tex]\( \frac{3}{5} \)[/tex].
- The y-intercept ([tex]\( b \)[/tex]) is [tex]\( -\frac{12}{5} \)[/tex].
In decimal form:
- The slope ([tex]\( m \)[/tex]) is [tex]\( 0.6 \)[/tex].
- The y-intercept ([tex]\( b \)[/tex]) is [tex]\( -2.4 \)[/tex].
So, the detailed answers are:
- The slope is [tex]\( \boxed{0.6} \)[/tex].
- The y-intercept is [tex]\( \boxed{-2.4} \)[/tex].
