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Zorluk: OrtaSlope of a Line

In the standard (x,y)(x, y) coordinate plane, a line passing through the points (−3,5)(-3, 5) and (1,−3)(1, -3) has a slope of −2-2. Is this statement true or false?

Cevap: Cevap

Cevap

True
The statement is true because substituting the coordinates (−3,5)(-3, 5) and (1,−3)(1, -3) into the slope formula m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1} yields m=−3−51−(−3)=−84=−2m = \frac{-3 - 5}{1 - (-3)} = \frac{-8}{4} = -2, which exactly matches the stated slope value.

Adım Adım Çözüm

1
Identify the coordinates of the two points on the line.
(x1,y1)=(−3,5)(x_1, y_1) = (-3, 5) and (x2,y2)=(1,−3)(x_2, y_2) = (1, -3)
The coordinates are needed to calculate the vertical change (rise) and horizontal change (run).
2
Apply the slope formula m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}.
m=−3−51−(−3)=−84=−2m = \frac{-3 - 5}{1 - (-3)} = \frac{-8}{4} = -2
Subtracting y1y_1 from y2y_2 yields the change in yy, and subtracting x1x_1 from x2x_2 yields the change in xx. Subtracting a negative number becomes addition: 1−(−3)=1+3=41 - (-3) = 1 + 3 = 4.
3
Compare the calculated slope to the value stated in the problem.
The calculated slope is −2-2, which matches the given statement.
Since the calculated value agrees with the statement, the statement is true.

Anahtar Kavram

Slope of a Line
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Konular

Slope of a Line

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