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Given a graph with points A and B, determine the coordinates of A and B, the gradient of line AB, and the equation of line AB in the form y = mx + c.
Mathematics
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3 partsStep-by-step solution
8 stepsPart a· 2 steps
Write the coordinates of points A and B.
Identify the coordinates of point A from the graph.
Point A is located at and .
Coordinates of A:Identify the coordinates of point B from the graph.
Point B is located at and .
Coordinates of B:
Part b-4
Determine the gradient of line AB.
Use the coordinates of points A and B.
Let
LetApply the gradient formula.
The gradient is given by the formula:
Substitute the coordinates into the formula.
The gradient of line AB is .
Part c
Determine the equation of line AB in the form .
Use the gradient (from part b) and one of the points, for example, point A .
The equation of a line can be written in the point-slope form: .
Substitute the gradient and the coordinates of point A into the point-slope form.
Simplify the equation to the form .
The equation of line AB is .
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