A line in the standard (x,y) coordinate plane passes through the points shown in the table below: | x | y | | :---: | :---: | | 0 | 5 | | 2 | 9 | | 4 | 13 | Which of the following equations represents this line?

A line in the standard (x,y) coordinate plane passes through the points shown in the table… — ACT

A line in the standard $(x,y)$ coordinate plane passes through the points shown in the table below:

Which of the following equations represents this line?

y = 2x + 5

The correct equation is

y = 2x + 5

because the slope of the line is

2

, calculated from the points

(0, 5)

and

(2, 9)

\frac{9 - 5}{2 - 0} = 2

, and the

y

-intercept is

5

, corresponding to the point

(0, 5)

Identify the

y

-intercept from the table.

The point

(0, 5)

indicates that the

y

-intercept is

5

, which means

b = 5

in the slope-intercept form

y = mx + b

The

y

-intercept is the point where the line crosses the

y

-axis, which occurs when

x = 0

Calculate the slope using two points from the table.

Using

(0, 5)

and

(2, 9)

, the slope

m = \frac{9 - 5}{2 - 0} = \frac{4}{2} = 2

The slope formula is the change in

y

divided by the change in

x

Substitute the slope and

y

-intercept into the slope-intercept equation.

Substituting

m = 2

and

b = 5

into

y = mx + b

yields

y = 2x + 5

This represents the linear relationship of the points.

Writing a linear equation in slope-intercept form from a table of values.

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