Math Problem Statement
Please complete the following questions on a separate sheet of paper.
Consider the following equations
y= 3x+5 B. y=3x
What are the slope and y-intercept for equation A?
What are the slope and y-intercept for equation B?
Solution
To solve these questions, let’s analyze the equations:
Equation A:
This is in the slope-intercept form , where:
- is the slope.
- is the y-intercept.
From :
- Slope:
- y-intercept:
Equation B:
This is also in the slope-intercept form .
From :
- Slope:
- y-intercept: (since there is no constant term, the y-intercept is 0).
Final Answers:
-
For Equation A:
- Slope =
- y-intercept =
-
For Equation B:
- Slope =
- y-intercept =
Would you like detailed explanations on finding slopes and intercepts?
Related Questions:
- How would the graph of differ from ?
- If , what is the value of when ?
- How does the slope affect the steepness of the lines in both equations?
- What are the points of intersection between the two lines and ?
- How would the equations change if the slopes were doubled?
Tip:
The slope determines the steepness and direction of a line, while the y-intercept determines where the line crosses the y-axis.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Slope-Intercept Form
Formulas
y = mx + b
Theorems
Slope-Intercept Form Theorem
Suitable Grade Level
Grades 7-9