Certainly! Let's analyze the linear equation given:
[tex]\[ y = -5x + 2 \][/tex]
We will determine the slope and the y-intercept from this equation.
### Step-by-Step Solution
1. Identify the Linear Equation Form:
- The given equation is [tex]\( y = -5x + 2 \)[/tex].
- This is in the form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] represents the slope and [tex]\( b \)[/tex] represents the y-intercept.
2. Determine the Slope (m):
- In the equation [tex]\( y = -5x + 2 \)[/tex], the coefficient of [tex]\( x \)[/tex] is [tex]\(-5\)[/tex].
- Therefore, the slope [tex]\( m \)[/tex] is [tex]\(-5\)[/tex].
3. Determine the Y-Intercept (b):
- In the equation [tex]\( y = -5x + 2 \)[/tex], the constant term is [tex]\( 2 \)[/tex].
- Therefore, the y-intercept [tex]\( b \)[/tex] is [tex]\( 2 \)[/tex].
### Conclusion
The slope of the line given by the equation [tex]\( y = -5x + 2 \)[/tex] is [tex]\(-5\)[/tex], and the y-intercept is [tex]\( 2 \)[/tex].
Thus, we have:
- Slope (m): [tex]\(-5\)[/tex]
- Y-Intercept (b): [tex]\( 2\)[/tex]
These values provide us with essential information about the line: it descends steeply (due to the negative slope) and crosses the y-axis at point [tex]\( (0, 2) \)[/tex].
