Math Problem Statement
Solution
The question asks for the equation of the line shown in slope-intercept form, which is:
Where:
- is the slope of the line, and
- is the y-intercept (the point where the line crosses the y-axis).
Step 1: Find the Slope ()
The slope is calculated as:
From the graph:
- One point on the line is , the y-intercept.
- Another point is .
Now, calculate the slope:
So, the slope .
Step 2: Find the Y-Intercept ()
The y-intercept is the point where the line crosses the y-axis. From the graph, this occurs at .
Step 3: Write the Equation
Substitute the values of and into the slope-intercept form:
Thus, the equation of the line is:
Do you want further details or have any questions about this?
Here are 5 related questions to deepen your understanding:
- What would happen if the slope was negative?
- How do you find the equation if you only know two points?
- How can you verify the correctness of the equation from the graph?
- What does the slope tell you about the direction of the line?
- How do you convert the equation to standard form?
Tip: The slope describes the rate of change of the line, telling you how steep the line is and its direction (positive or negative slope).
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Math Problem Analysis
Mathematical Concepts
Algebra
Equations of Lines
Graphing
Formulas
y = mx + b
Slope formula: m = (y2 - y1) / (x2 - x1)
Theorems
Slope-intercept form
Suitable Grade Level
Grades 8-10