Math Problem Statement

Identify the the slope and Y-intercept on the of the line y=2x+17y=2x+17 

Solution

The given equation of the line is:

y=2x+17y = 2x + 17

This is in the slope-intercept form of a linear equation, which is generally written as:

y=mx+by = mx + b

where:

  • mm is the slope of the line,
  • bb is the y-intercept.

For the equation y=2x+17y = 2x + 17, we can identify the following:

  • Slope (m) = 2
  • Y-intercept (b) = 17

This means the slope of the line is 2, and the line crosses the y-axis at y=17y = 17.

Would you like more details on how to interpret this, or have any other questions related to linear equations?

Here are five questions that expand on the concept:

  1. How do you graph the line y=2x+17y = 2x + 17?
  2. What happens to the slope if the equation changes to y=3x+5y = -3x + 5?
  3. How can you write an equation of a line given the slope and y-intercept?
  4. How do you determine the slope when given two points on the line?
  5. What is the significance of the slope and y-intercept in real-life applications?

Tip: The slope represents the steepness of the line, and the y-intercept tells you where the line crosses the y-axis, which is particularly useful for graphing linear equations.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Slope-Intercept Form

Formulas

y = mx + b

Theorems

Slope-Intercept Theorem

Suitable Grade Level

Grades 7-9