Answered

Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Discover the answers you need from a community of experts ready to help you with their knowledge and experience in various fields. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

Which statements are true about the linear inequality [tex][tex]$y \ \textgreater \ \frac{3}{4} x - 2$[/tex][/tex]? Select three options.

A. The slope of the line is -2.
B. The graph of [tex][tex]$y \ \textgreater \ \frac{3}{4} x - 2$[/tex][/tex] is a dashed line.
C. The area below the line is shaded.
D. One solution to the inequality is [tex]$(0,0)$[/tex].
E. The graph intercepts the [tex]$y$[/tex]-axis at [tex]$(0,-2)$[/tex].

Sagot :

GinnyAnswer
Let's analyze each statement step-by-step in the context of the linear inequality [tex]\( y > \frac{3}{4} x - 2 \)[/tex]:

### Statement 1: "The slope of the line is -2."
- The given inequality is [tex]\( y > \frac{3}{4} x - 2 \)[/tex].
- The standard form for a linear equation is [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope.
- Here, the slope [tex]\( m \)[/tex] is [tex]\(\frac{3}{4}\)[/tex], not -2.
- This statement is false.

### Statement 2: "The graph of [tex]\( y > \frac{3}{4} x - 2 \)[/tex] is a dashed line."
- For [tex]\( y > \frac{3}{4} x - 2 \)[/tex], the line [tex]\( y = \frac{3}{4} x - 2 \)[/tex] represents the boundary.
- When graphing inequalities with a "greater than" (>) or "less than" (<), the line is dashed to indicate that points on the line are not included in the solution.
- This statement is true.

### Statement 3: "The area below the line is shaded."
- The inequality [tex]\( y > \frac{3}{4} x - 2 \)[/tex] indicates that we are interested in the region above the line because we want values of [tex]\( y \)[/tex] that are greater than what the line gives for corresponding [tex]\( x \)[/tex] values.
- Therefore, the area above the line should be shaded, not below.
- This statement is false.

### Statement 4: "One solution to the inequality is [tex]\( (0,0) \)[/tex]."
- To check if a point is a solution to the inequality, substitute [tex]\( x = 0 \)[/tex] and [tex]\( y = 0 \)[/tex] into the inequality.
- [tex]\( 0 > \frac{3}{4}(0) - 2 \implies 0 > -2 \)[/tex], which is true.
- Therefore, [tex]\( (0,0) \)[/tex] is indeed a solution.
- This statement is true.

### Statement 5: "The graph intercepts the [tex]\( y \)[/tex]-axis at [tex]\( (0,-2) \)[/tex]."
- The [tex]\( y \)[/tex]-intercept of a line occurs where [tex]\( x = 0 \)[/tex].
- Substituting [tex]\( x = 0 \)[/tex] into [tex]\( y = \frac{3}{4} x - 2 \)[/tex], we get [tex]\( y = -2 \)[/tex].
- Therefore, the line intercepts the [tex]\( y \)[/tex]-axis at [tex]\( (0, -2) \)[/tex].
- This statement is true.

### Conclusion
True statements about the linear inequality [tex]\( y > \frac{3}{4} x - 2 \)[/tex] are:
- The graph of [tex]\( y > \frac{3}{4} x - 2 \)[/tex] is a dashed line.
- One solution to the inequality is [tex]\( (0,0) \)[/tex].
- The graph intercepts the [tex]\( y \)[/tex]-axis at [tex]\( (0, -2) \)[/tex].

So, the three true statements are:
1. The graph of [tex]\( y > \frac{3}{4} x - 2 \)[/tex] is a dashed line.
2. One solution to the inequality is [tex]\( (0,0) \)[/tex].
3. The graph intercepts the [tex]\( y \)[/tex]-axis at [tex]\( (0,-2) \)[/tex].
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.