Math Problem Statement
Solution
Let's analyze the image.
The task is to write the equation of the line in fully simplified slope-intercept form. The slope-intercept form of a line is:
where:
- is the slope of the line.
- is the y-intercept (the value of when ).
Step 1: Identify two points on the line
Looking at the graph:
- One point is .
- Another point is .
Step 2: Calculate the slope
The formula for slope between two points and is:
Using the points and :
Step 3: Find the y-intercept
From the graph, the y-intercept is (since the line crosses the y-axis at ).
Step 4: Write the equation
Now that we have the slope and the y-intercept , the equation of the line in slope-intercept form is:
This is the required equation.
Do you need further clarification or have any questions?
Here are 5 related questions:
- How do you convert between slope-intercept form and standard form?
- What does the slope represent in real-world applications?
- How can you determine if two lines are parallel or perpendicular?
- How do you find the x-intercept of a line from its equation?
- What happens to the graph of a line if the slope increases?
Tip: When finding the slope between two points, always pay attention to the signs to avoid calculation errors.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Slope-Intercept Form
Formulas
y = mx + b
Slope formula: m = (y2 - y1) / (x2 - x1)
Theorems
Slope-Intercept Form
Suitable Grade Level
Grades 8-10
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