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: y=3x+5y = 3x + 5

This is in the slope-intercept form y=mx+by = mx + b, where:

  • mm is the slope.
  • bb is the y-intercept.

From y=3x+5y = 3x + 5:

  • Slope: m=3m = 3
  • y-intercept: b=5b = 5

Equation B: y=3xy = 3x

This is also in the slope-intercept form y=mx+by = mx + b.

From y=3xy = 3x:

  • Slope: m=3m = 3
  • y-intercept: b=0b = 0 (since there is no constant term, the y-intercept is 0).

Final Answers:

  1. For Equation A:

    • Slope = 33
    • y-intercept = 55
  2. For Equation B:

    • Slope = 33
    • y-intercept = 00

Would you like detailed explanations on finding slopes and intercepts?


Related Questions:

  1. How would the graph of y=3x+5y = 3x + 5 differ from y=3xy = 3x?
  2. If y=3x+5y = 3x + 5, what is the value of yy when x=2x = -2?
  3. How does the slope affect the steepness of the lines in both equations?
  4. What are the points of intersection between the two lines y=3x+5y = 3x + 5 and y=3xy = 3x?
  5. 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.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

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