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Asked by Aamir Last Modified
Answer Line Passing through (2,3) and (3,2) - Coordinates of Intercepts
Formula for Slope (m): m=y2−y1x2−x1m=x2−x1y2−y1
Given Points: P1(x1,y1)=(2,3)P1(x1,y1)=(2,3) P2(x2,y2)=(3,2)P2(x2,y2)=(3,2)
Calculation: m=2−33−2=−1m=3−22−3=−1
Point-Slope Form: y−y1=m⋅(x−x1)y−y1=m⋅(x−x1)
Substitute Values: y−3=−1⋅(x−2)y−3=−1⋅(x−2)
Simplify: y=−x+1y=−x+1
Definition: The x-intercept is where the line crosses the x-axis (y=0y=0).
Substitute y=0y=0 in the Equation: 0=−x+10=−x+1
Solve for x: x=1x=1
Coordinates of x-Intercept: (1,0)(1,0)
Definition: The y-intercept is where the line crosses the y-axis (x=0x=0).
Substitute x=0x=0 in the Equation: y=−0+1y=−0+1
Coordinates of y-Intercept: (0,1)(0,1)
Equation of the Line: y=−x+1y=−x+1
x-Intercept: (1,0)(1,0)
y-Intercept: (0,1)(0,1)
This completes the analysis of the line passing through the points (2,3) and (3,2) with the determination of the x and y intercepts.
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