Math Problem Statement
The gradient of the following line is
Solution
The gradient (or slope) of a line can be calculated using the formula:
Here, we can see from the graph that one point on the line is . We can also assume that another point on the line passes through the origin, .
Using these two points, we apply the formula:
Thus, the gradient (slope) of the line is:
Would you like any further details or explanations?
Here are 5 related questions to expand your understanding:
- How would the slope change if the line passed through a different point?
- What is the equation of the line in slope-intercept form using this slope?
- How do you interpret a negative slope in terms of the line's direction?
- Can you calculate the length of the line segment between two points on this line?
- How would you find the x-intercept and y-intercept of this line?
Tip: The steeper the line, the larger the magnitude of the slope. Positive slopes rise from left to right, while negative slopes fall from left to right.
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Math Problem Analysis
Mathematical Concepts
Algebra
Analytic Geometry
Slope of a Line
Formulas
m = (y2 - y1) / (x2 - x1)
Theorems
Slope Formula
Suitable Grade Level
Grades 8-10
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