Math Problem Statement

Graph the following features: - Y-intercept = 6 - Slope = 2

Solution

The image provides the features for a linear equation:

  1. Y-intercept = 6: This means the line passes through the point (0,6)(0, 6) on the yy-axis.
  2. Slope = 2: This means for every 1 unit increase in xx, yy increases by 2 units.

Steps to Graph:

  1. Plot the y-intercept: Place a point at (0,6)(0, 6) on the graph.
  2. Use the slope: From (0,6)(0, 6), move 1 unit to the right (positive xx) and 2 units up (positive yy) to get another point at (1,8)(1, 8).
  3. Draw the line: Connect the points (0,6)(0, 6) and (1,8)(1, 8), and extend the line in both directions.

The equation for this line is: y=2x+6y = 2x + 6

Would you like a detailed explanation of how to calculate the slope or use the slope-intercept form?


Here are five follow-up questions related to this topic:

  1. What does the slope of 2 represent in this graph?
  2. How can you find the equation of a line given two points?
  3. What would the graph look like if the slope were negative?
  4. How would the graph change if the yy-intercept were 0?
  5. Can you determine the slope from a graph without the equation?

Tip: When graphing a line, always double-check the slope direction (positive/negative) to ensure accuracy!

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Graphing
Slope-Intercept Form

Formulas

y = mx + b (Slope-Intercept Form)

Theorems

Slope Definition (Rise over Run)

Suitable Grade Level

Grades 7-9