To determine the properties of the given linear equation [tex]\( y = -\frac{3}{5}x - 2 \)[/tex], we need to analyze the equation in its slope-intercept form, which is given by [tex]\( y = mx + b \)[/tex].
1. Understanding the Slope-Intercept Form:
- The slope-intercept form of a linear equation is [tex]\( y = mx + b \)[/tex].
- Here, [tex]\( m \)[/tex] represents the slope of the line.
- [tex]\( b \)[/tex] represents the y-intercept of the line, which is the value of [tex]\( y \)[/tex] when [tex]\( x = 0 \)[/tex].
2. Identifying the Slope and Y-Intercept:
- In the given equation [tex]\( y = -\frac{3}{5}x - 2 \)[/tex]:
- The coefficient of [tex]\( x \)[/tex] is [tex]\( -\frac{3}{5} \)[/tex]. Thus, the slope [tex]\( m \)[/tex] is [tex]\( -\frac{3}{5} \)[/tex].
- The constant term is [tex]\( -2 \)[/tex]. Thus, the y-intercept [tex]\( b \)[/tex] is [tex]\( -2 \)[/tex].
3. Summary of Findings:
- The y-intercept is [tex]\( -2 \)[/tex].
- The slope is [tex]\( -\frac{3}{5} \)[/tex].
Now, let's relate these findings to the options given in the question.
Evaluating the Statements:
1. The [tex]\( y \)[/tex]-intercept is [tex]\(-\frac{3}{5}\)[/tex]:
- This statement is Incorrect. The y-intercept is [tex]\( -2 \)[/tex], not [tex]\( -\frac{3}{5} \)[/tex].
2. The [tex]\( y \)[/tex]-intercept is [tex]\( 2 \)[/tex]:
- This statement is Incorrect. The y-intercept is [tex]\( -2 \)[/tex], not [tex]\( 2 \)[/tex].
3. The [tex]\( y \)[/tex]-intercept is [tex]\( -2 \)[/tex]:
- This statement is Correct. The y-intercept of the equation is indeed [tex]\( -2 \)[/tex].
4. The slope is [tex]\(-\frac{3}{5}\)[/tex]:
- This statement is Correct. The slope of the equation is indeed [tex]\( -\frac{3}{5} \)[/tex].
5. The slope is [tex]\( 2 \)[/tex]:
- This statement is Incorrect. The slope is [tex]\( -\frac{3}{5} \)[/tex], not [tex]\( 2 \)[/tex].
6. The slope is [tex]\( -2 \)[/tex]:
- This statement is Incorrect. The slope is [tex]\( -\frac{3}{5} \)[/tex], not [tex]\( -2 \)[/tex].
Conclusion:
From the given linear equation [tex]\( y = -\frac{3}{5}x - 2 \)[/tex], the correct statements are:
- The y-intercept is [tex]\( -2 \)[/tex].
- The slope is [tex]\( -\frac{3}{5} \)[/tex].
