Math Problem Statement
Solution
The graph in the image shows a straight line, and we are asked to write the equation of the line where depends on .
To write the equation of a straight line, we use the slope-intercept form:
Where:
- is the slope of the line, and
- is the y-intercept (the point where the line crosses the y-axis).
Step 1: Identify the y-intercept ()
From the graph, the line crosses the y-axis at , so:
Step 2: Calculate the slope ()
The slope is the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.
From the graph, two clear points are:
- (the y-intercept)
The slope is calculated as follows:
Step 3: Write the equation
Now that we know the slope and the y-intercept , the equation of the line is:
Would you like further clarification, or do you have any questions?
Here are five related questions for practice:
- What is the equation of a line with slope and y-intercept ?
- If the line passes through points and , how do you find its equation?
- How do you determine the slope of a line given its equation in standard form ?
- What is the slope of a line parallel to ?
- How would the equation change if the line were shifted 3 units down?
Tip: When finding the slope, always carefully pick points where the line crosses grid intersections for more accurate calculations.
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Slope-Intercept Form
Formulas
y = mx + b
Theorems
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Suitable Grade Level
Grades 8-10