In the standard (x, y) coordinate plane, a line is defined by the equation 2x + 3y = 22. A… — ACT

In the standard $(x, y)$ coordinate plane, a line is defined by the equation $2x + 3y = 22$ . A second line passes through the origin $(0, 0)$ and intersects the first line at a point where $x = 5$ . What is the slope of this second line?

Cevap: 0.8

Cevap

The slope of the second line is

0.8

(or

\frac{4}{5}

The intersection point has an

x

-coordinate of

5

. Substituting this into

2x + 3y = 22

gives

2(5) + 3y = 22

, which simplifies to

3y = 12

, or

y = 4

. Thus, the intersection point is

(5, 4)

. The second line passes through

(0, 0)

and

(5, 4)

. Using the slope formula, the slope is

\frac{4 - 0}{5 - 0} = 0.8

Adım Adım Çözüm

Substitute

x = 5

into the equation of the first line to find the

y

-coordinate of the intersection point.

The intersection point is

(5, 4)

Since the two lines intersect at

x = 5

, the intersection point must satisfy the equation of the first line.

Use the slope formula to find the slope of the line connecting

(0, 0)

and

(5, 4)

The slope is

0.8

The second line passes through the origin

(0, 0)

and the intersection point

(5, 4)

, so its slope is the ratio of the change in

y

to the change in

x

Anahtar Kavram

Finding the slope of a line given two points on the coordinate plane, where one point is determined by the intersection of two linear paths.

Alternatif Yöntem

Since the second line passes through the origin

(0, 0)

, its equation is of the form

y = mx

, where

m

is the slope. At the intersection point

(5, y)

, we have

y = 5m

. We can substitute this directly into the first line's equation:

2x + 3y = 22 \Rightarrow 2(5) + 3(5m) = 22 \Rightarrow 10 + 15m = 22 \Rightarrow 15m = 12 \Rightarrow m = \frac{12}{15} = 0.8

Tahmini Süre:1m 30s

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Adım Adım Çözüm

Anahtar Kavram

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Alternatif Yöntem

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