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Select the correct graph of the equation: y = 3a + 1 O O O ka 2 2 y NO 46 2

Select the correct graph of the equation: y = 3a + 1 O O O ka 2 2 y NO 46 2

Algebra and Trigonometry (6th Edition)
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 12 Select the correct graph of the equation: \( y = 3x + 1 \) There are four options given below, each featuring a coordinate plane with a graphed line. Your task is to identify which graph correctly represents the equation \( y = 3x + 1 \). #### Graph Description: 1. **Option 1:** - The line appears to have a positive slope. - The y-intercept is at \( y = 1 \). - Points where the graph intersects the grid lines are at coordinates consistent with the slope \( 3 \) (rise over run: increasing by 3 units vertically for every 1 unit horizontally). 2. **Option 2:** - The line appears to intersect the y-axis at \( y = -1 \). - The slope looks to be negative. 3. **Option 3:** - The line has a positive slope. - Intersects the y-axis at \( y = 1 \), similar to the correct y-intercept from the equation. 4. **Option 4:** - The line intersects the y-axis at \( y = -2 \). - The slope is negative. From these descriptions, the correct graph would intersect the y-axis at \( y = 1 \) and have a positive slope (3:1 ratio). Options 1 and 3 meet the y-intercept condition, but we need to ensure the slope is correct. Upon further inspection, **Option 1** has a slope of 3 and the correct y-intercept (\( y = 1 \)). Thus, **Option 1** is the correct graph of the equation \( y = 3x + 1 \).
Transcribed Image Text:### Question 12 Select the correct graph of the equation: \( y = 3x + 1 \) There are four options given below, each featuring a coordinate plane with a graphed line. Your task is to identify which graph correctly represents the equation \( y = 3x + 1 \). #### Graph Description: 1. **Option 1:** - The line appears to have a positive slope. - The y-intercept is at \( y = 1 \). - Points where the graph intersects the grid lines are at coordinates consistent with the slope \( 3 \) (rise over run: increasing by 3 units vertically for every 1 unit horizontally). 2. **Option 2:** - The line appears to intersect the y-axis at \( y = -1 \). - The slope looks to be negative. 3. **Option 3:** - The line has a positive slope. - Intersects the y-axis at \( y = 1 \), similar to the correct y-intercept from the equation. 4. **Option 4:** - The line intersects the y-axis at \( y = -2 \). - The slope is negative. From these descriptions, the correct graph would intersect the y-axis at \( y = 1 \) and have a positive slope (3:1 ratio). Options 1 and 3 meet the y-intercept condition, but we need to ensure the slope is correct. Upon further inspection, **Option 1** has a slope of 3 and the correct y-intercept (\( y = 1 \)). Thus, **Option 1** is the correct graph of the equation \( y = 3x + 1 \).
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