In the standard (x, y) coordinate plane, a line passes through the points (1, 3) and (4, 9… — ACT

In the standard $(x, y)$ coordinate plane, a line passes through the points $(1, 3)$ and $(4, 9)$ . Is the statement that this line has a slope of $2$ true or false?

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Cevap

true

Applying the slope formula

m = \frac{y_2 - y_1}{x_2 - x_1}

to the points

(1, 3)

and

(4, 9)

yields

\frac{9 - 3}{4 - 1} = \frac{6}{3} = 2

, which confirms that the statement is true.

Adım Adım Çözüm

Identify the coordinates of the two points on the line.

The points are

(x_1, y_1) = (1, 3)

and

(x_2, y_2) = (4, 9)

These coordinates are needed to apply the slope formula.

Apply the slope formula

m = \frac{y_2 - y_1}{x_2 - x_1}

using the identified points.

m = \frac{9 - 3}{4 - 1} = \frac{6}{3} = 2

This calculates the rate of change of the line, which is its slope.

Compare the calculated slope to the value in the statement.

The calculated slope is

2

, which matches the statement.

To determine whether the statement is true or false.

Anahtar Kavram

The slope of a line is the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line.

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Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

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