A linear relationship between x and y is defined by the values in the table below. | x | y | | :--- | :--- | | 2 | 7 | | 4 | 13 | | 6 | 19 | Which of the following equations represents this relationship?

A linear relationship between x and y is defined by the values in the table below. | x | y… — SAT

A linear relationship between $x$ and $y$ is defined by the values in the table below.

$x$	$y$
2	7
4	13
6	19

Which of the following equations represents this relationship?

A
$y = 3x - 5$
B
$y = \frac{1}{3}x + \frac{19}{3}$
$y = 3x + 1$ Cevap
D
$y = 6x - 5$

Cevap

The equation representing the relationship is

y = 3x + 1

The correct equation is

y = 3x + 1

. The slope

m

of the linear function can be determined from the table values

(2, 7)

and

(4, 13)

\frac{13 - 7}{4 - 2} = \frac{6}{2} = 3

. Substituting the slope

m = 3

and the point

(2, 7)

into the slope-intercept form

y = mx + b

gives

7 = 3(2) + b

, which simplifies to

7 = 6 + b

, so

b = 1

. Therefore, the equation is

y = 3x + 1

Adım Adım Çözüm

Find the slope (

m

) of the linear relationship using the points

(2, 7)

and

(4, 13)

from the table.

m = 3

The slope is the ratio of the change in

y

to the change in

x

between any two points on the line:

m = \frac{13 - 7}{4 - 2} = \frac{6}{2} = 3

Use the slope

m = 3

and the point

(2, 7)

to find the

y

-intercept (

b

) of the line.

b = 1

Substituting the coordinates and slope into the slope-intercept equation

y = mx + b

gives

7 = 3(2) + b

, which simplifies to

7 = 6 + b

, leading to

b = 1

Substitute the slope and

y

-intercept into the slope-intercept form.

y = 3x + 1

Combining the slope of

3

and

y

-intercept of

1

yields the equation

y = 3x + 1

Anahtar Kavram

Determining a linear equation from a table of values

Tahmini Süre:45s

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

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