The image contains four graphs, each displaying a straight line plotted on a Cartesian coordinate system ranging from -10 to 10 on both the x and y axes. Below is a detailed description of each graph:1. **Graph 1:** - The line passes through the origin (0,0) with a positive slope. It moves upwards from the bottom left towards the top right of the graph. - This indicates a direct relationship between the x and y values, where both increase together.2. **Graph 2:** - The line has a negative slope, moving from the top left towards the bottom right of the graph. - This suggests an inverse relationship, where y decreases as x increases.3. **Graph 3:** - Similar to Graph 1, this line also has a positive slope and passes through the origin. - It reflects a proportional increase between x and y values.4. **Graph 4:** - The line has a positive slope but passes through (0, -10) on the y-axis. - This indicates a linear relationship with a y-intercept of -10, shifting the entire line downwards compared to the origin-based lines in Graphs 1 and 3.These graphs are useful for understanding the basic concepts of linear relationships and the effects of different slopes and intercepts on a line’s position in the coordinate plane. **Graph the Linear Function Using the Slope and Y-intercept**Equation given: \( y = \frac{1}{2}x + 5 \)**Explanation of Graphs:**The task is to graph the linear equation using the slope (\( \frac{1}{2} \)) and the y-intercept (5).1. **First Graph:** - The line intersects the y-axis at 5, which is correct according to the y-intercept given in the equation. - The slope of \( \frac{1}{2} \) is visualized as the line moves up by 1 unit for every 2 units it moves to the right.2. **Second Graph:** - This graph also displays a line through the point (0, 5) on the y-axis. - The slope appears consistent with \( \frac{1}{2} \) as it rises by 1 unit for every 2 units moved to the right.3. **Third Graph:** - The line does not align with the correct y-intercept or slope. - It intersects the y-axis at a different point and has a negative slope, indicating an incorrect representation of the equation.The correct graph for the equation \( y = \frac{1}{2}x + 5 \) is the one where the line passes through the y-axis at 5 and follows a slope pattern of rising 1 unit vertically for every 2 units horizontally. The first two graphs align with these criteria.

Answered: Graph the linear function using the…

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Graph the linear function using the slope and y-intercept. y = x + 5 11/12

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

The image contains four graphs, each displaying a straight line plotted on a Cartesian coordinate system ranging from -10 to 10 on both the x and y axes. Below is a detailed description of each graph:

1. **Graph 1:**
- The line passes through the origin (0,0) with a positive slope. It moves upwards from the bottom left towards the top right of the graph.
- This indicates a direct relationship between the x and y values, where both increase together.

2. **Graph 2:**
- The line has a negative slope, moving from the top left towards the bottom right of the graph.
- This suggests an inverse relationship, where y decreases as x increases.

3. **Graph 3:**
- Similar to Graph 1, this line also has a positive slope and passes through the origin.
- It reflects a proportional increase between x and y values.

4. **Graph 4:**
- The line has a positive slope but passes through (0, -10) on the y-axis.
- This indicates a linear relationship with a y-intercept of -10, shifting the entire line downwards compared to the origin-based lines in Graphs 1 and 3.

These graphs are useful for understanding the basic concepts of linear relationships and the effects of different slopes and intercepts on a line’s position in the coordinate plane.

**Graph the Linear Function Using the Slope and Y-intercept**

Equation given: \( y = \frac{1}{2}x + 5 \)

**Explanation of Graphs:**

The task is to graph the linear equation using the slope (\( \frac{1}{2} \)) and the y-intercept (5).

1. **First Graph:**
- The line intersects the y-axis at 5, which is correct according to the y-intercept given in the equation.
- The slope of \( \frac{1}{2} \) is visualized as the line moves up by 1 unit for every 2 units it moves to the right.

2. **Second Graph:**
- This graph also displays a line through the point (0, 5) on the y-axis.
- The slope appears consistent with \( \frac{1}{2} \) as it rises by 1 unit for every 2 units moved to the right.

3. **Third Graph:**
- The line does not align with the correct y-intercept or slope.
- It intersects the y-axis at a different point and has a negative slope, indicating an incorrect representation of the equation.

The correct graph for the equation \( y = \frac{1}{2}x + 5 \) is the one where the line passes through the y-axis at 5 and follows a slope pattern of rising 1 unit vertically for every 2 units horizontally. The first two graphs align with these criteria.

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