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Answer:
- x-intercept: (-5, 0)
- y-intercept: (0, 4)
- perpendicular: 5x +4y = 0
Step-by-step explanation:
Each of the intercepts is found by setting the other variable to zero and solving for the intercept value.
x-intercept
4x -5·0 +20 = 0
x +20/4 = 0 . . . . . divide by the coefficient of x
x = -5 . . . . . . . . . . add -5
The x-intercept point is (-5, 0).
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y-intercept
4·0 -5y +20 = 0
y +20/-5 = 0 . . . . . divide by the coefficient of y
y = 4 . . . . . . . . . . . add 4
The y-intercept point is (0, 4).
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The perpendicular line is found by swapping the x- and y-coefficients, negating one of them. You want the leading coefficient positive, so the equation becomes ...
5x +4y = (some constant)
The constant is chosen according to the point you want on the line. For a line through the origin, the constant is zero.
5x +4y = 0 . . . . perpendicular line
