Math Problem Statement
Solution
To determine the equation of the line in slope-intercept form , where is the slope and is the y-intercept, follow these steps:
Step 1: Find the Slope ()
The slope is calculated as:
From the graph, identify two points on the line:
- Point 1:
- Point 2:
Now substitute into the slope formula:
The slope is .
Step 2: Find the Y-Intercept ()
The y-intercept is the point where the line crosses the -axis. From the graph, the line crosses the -axis at .
Thus, .
Step 3: Write the Equation
Substitute the slope and y-intercept into the slope-intercept form :
Final Answer:
The equation of the line in slope-intercept form is:
Do you want me to explain how to verify the slope or graph the equation? Let me know if you have more questions!
Related Questions:
- How can you calculate the slope if only the graph is provided?
- What is the general form of a linear equation, and how does it relate to slope-intercept form?
- How do you determine the slope if the line passes through vertical or horizontal axes?
- Can you graph a line given its equation in slope-intercept form?
- How does changing the slope affect the steepness of the line?
Tip:
Always choose two clear points from a graph to calculate the slope accurately!
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Slope-Intercept Form
Graphing Lines
Formulas
Slope formula: m = (y2 - y1) / (x2 - x1)
Slope-intercept form: y = mx + b
Theorems
The slope-intercept form theorem: A linear equation can be expressed as y = mx + b
Suitable Grade Level
Grades 8-10