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Zorluk: OrtaSlope of a Line

In the standard (x,y)(x, y) coordinate plane, if a line passes through the point (1,3)(1, 3) and has an undefined slope, then the point (1,−5)(1, -5) lies on this line.

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The statement is true because a line with an undefined slope is a vertical line, meaning all points on the line share the same x-coordinate. Since the line passes through (1,3)(1, 3), the x-coordinate of all points on the line is 11, which includes the point (1,−5)(1, -5).
A line with an undefined slope is a vertical line. Since it passes through (1,3)(1, 3), the x-coordinate of every point on this line must be 11. The point (1,−5)(1, -5) has an x-coordinate of 11, so it lies on this vertical line, making the statement true.

Adım Adım Çözüm

1
Identify the geometric properties of a line with an undefined slope.
A line with an undefined slope is a vertical line.
The slope formula is m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}. The slope is undefined when the denominator, representing the change in xx, is equal to zero. This occurs only for vertical lines.
2
Determine the equation of the vertical line that passes through the point (1,3)(1, 3).
The equation of the line is x=1x = 1.
Since the line is vertical, all points on the line share the same x-coordinate as the given point (1,3)(1, 3).
3
Verify if the point (1,−5)(1, -5) satisfies the equation of the line.
The x-coordinate of the point (1,−5)(1, -5) is 11, which satisfies the equation x=1x = 1.
A point lies on a line if its coordinates satisfy the equation of the line.

Anahtar Kavram

Slope of a Line
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Konular

Slope of a Line

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