To determine which linear equation has a slope of 3 and a y-intercept of -2, we'll use the standard form of a linear equation which is:
[tex]\[ y = mx + b \][/tex]
where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
Given:
- The slope [tex]\( m \)[/tex] is 3.
- The y-intercept [tex]\( b \)[/tex] is -2.
Substitute these values into the standard linear equation:
[tex]\[ y = 3x - 2 \][/tex]
Now, let's examine the provided choices to see which one matches this equation:
1. [tex]\( y = 3x + 2 \)[/tex]
2. [tex]\( y = 3x - 2 \)[/tex]
3. [tex]\( y = -2x + 3 \)[/tex]
4. [tex]\( y = -2x - 3 \)[/tex]
The correct equation, [tex]\( y = 3x - 2 \)[/tex], matches the second choice provided in the list.
Therefore, the correct choice is:
[tex]\[ y = 3x - 2 \][/tex]
Thus, the correct answer is the second option on the list:
[tex]\[ 1 \][/tex]
