Math Problem Statement
Graph the following features:
- Y-intercept = 6
- Slope = 2
Solution
The image provides the features for a linear equation:
- Y-intercept = 6: This means the line passes through the point on the -axis.
- Slope = 2: This means for every 1 unit increase in , increases by 2 units.
Steps to Graph:
- Plot the y-intercept: Place a point at on the graph.
- Use the slope: From , move 1 unit to the right (positive ) and 2 units up (positive ) to get another point at .
- Draw the line: Connect the points and , and extend the line in both directions.
The equation for this line is:
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:
- What does the slope of 2 represent in this graph?
- How can you find the equation of a line given two points?
- What would the graph look like if the slope were negative?
- How would the graph change if the -intercept were 0?
- 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