Math Problem Statement
Solution
The image provided contains a question regarding finding the equation of a straight line based on the given graph.
Here's a summary of the steps:
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Calculate the gradient of the line: Two points on the line are given: (0, 4) and (2, 8). The gradient (slope) formula is: So, the gradient .
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State the y-intercept of the straight line: The y-intercept occurs when . From the point (0, 4), we see that the y-intercept is 4.
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Write the equation of the line in the form : Using the gradient and the y-intercept , the equation of the line is:
This is the required equation of the straight line.
Would you like any additional details or clarifications on this? Here are five relative questions:
- How do we generalize the equation of any straight line?
- What does the gradient represent geometrically on a graph?
- Can you explain why the y-intercept occurs when ?
- How would the equation change if the line had a negative gradient?
- How do we find the x-intercept from the equation of a straight line?
Tip: When finding the gradient of a line, always ensure you're using two distinct points on the line and applying the formula correctly to avoid sign errors.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Formulas
Gradient (m) formula: m = (y2 - y1) / (x2 - x1)
Linear equation: y = mx + c
Theorems
Slope-Intercept Form of a Line
Suitable Grade Level
Grades 8-10