Math Problem Statement
Find the gradient of the line joining (3,-2) and (5, 3). What is the equation of this line?
Solution
Step 1: Find the Gradient of the Line
The formula to calculate the gradient (or slope) of a line passing through two points and is:
For the points and , let:
Now, applying the formula:
So, the gradient of the line is .
Step 2: Find the Equation of the Line
The equation of a line in slope-intercept form is:
Where:
- is the gradient
- is the y-intercept
We already know that the gradient . To find , we can substitute one of the points into the equation.
Using the point :
Thus, the equation of the line is:
Final Answer:
- The gradient of the line is .
- The equation of the line is .
Would you like any further details or have any questions? Here are some related questions:
- How do you interpret the meaning of the gradient in this context?
- What would the equation of the line look like in standard form?
- How can you find the x-intercept of this line?
- How would you graph this line on the coordinate plane?
- What happens to the equation of the line if the points were switched?
Tip: When calculating the gradient of a line, always make sure to subtract the y-coordinates and x-coordinates in the correct order to avoid sign errors.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Slope
Coordinate Geometry
Formulas
Gradient formula: m = (y2 - y1) / (x2 - x1)
Equation of line: y = mx + c
Theorems
-
Suitable Grade Level
Grades 7-9
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