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Zorluk: KolayCoordinate Geometry and Lines

In the xyxy-plane, line mm passes through the point (4,−2)(4, -2) and has a yy-intercept of 66. What is the slope of line mm?

Cevap: -2

Cevap

The slope of line mm is −2-2.
The yy-intercept of 66 indicates that the line passes through (0,6)(0, 6). Substituting (0,6)(0, 6) and (4,−2)(4, -2) into the slope formula yields m=6−(−2)0−4=8−4=−2m = \frac{6 - (-2)}{0 - 4} = \frac{8}{-4} = -2.

Adım Adım Çözüm

1
Identify the coordinates of two points on line mm.
The line passes through (4,−2)(4, -2) and the yy-intercept point (0,6)(0, 6).
The yy-intercept is the point where x=0x = 0.
2
Apply the slope formula m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}.
Substitute (x1,y1)=(4,−2)(x_1, y_1) = (4, -2) and (x2,y2)=(0,6)(x_2, y_2) = (0, 6) into the formula: m=6−(−2)0−4m = \frac{6 - (-2)}{0 - 4}.
Slope represents the ratio of vertical change to horizontal change between two points on a line.
3
Simplify the fractional expression.
m=8−4=−2m = \frac{8}{-4} = -2.
Dividing positive 88 by negative 44 gives −2-2.

Anahtar Kavram

Slope of a line given two points or a point and intercept
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