The table below shows coordinate points (x, y) that lie on a line L in the standard (x, y)… — ACT

The table below shows coordinate points $(x, y)$ that lie on a line $L$ in the standard $(x, y)$ coordinate system:

What is the $x$ -intercept of line $L$ ?

The correct answer is

\frac{1}{3}

The correct answer is

\frac{1}{3}

. First, find the slope of the line using the points

(-2, -7)

and

(1, 2)

from the table:

m = \frac{2 - (-7)}{1 - (-2)} = 3

. Next, substitute the slope and the coordinate point

(1, 2)

into the point-slope equation to get

y - 2 = 3(x - 1)

, which simplifies to

y = 3x - 1

. To find the

x

-intercept, set

y = 0

and solve for

x

0 = 3x - 1

, which gives

x = \frac{1}{3}

Calculate the slope (

m

) of line

L

using the coordinate points

(-2, -7)

and

(1, 2)

from the table.

The slope is

m = \frac{2 - (-7)}{1 - (-2)} = \frac{9}{3} = 3

The slope of a line represents its constant rate of change and is calculated using the formula

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

Write the linear equation in slope-intercept form using the slope

m = 3

and the point

(1, 2)

Using the point-slope form:

y - 2 = 3(x - 1) \Rightarrow y - 2 = 3x - 3 \Rightarrow y = 3x - 1

Using point-slope form

y - y_1 = m(x - x_1)

allows us to easily simplify the relationship into slope-intercept form

y = mx + b

Find the

x

-intercept of the line by setting

y = 0

and solving the equation for

x

Setting

y = 0

gives

0 = 3x - 1 \Rightarrow 3x = 1 \Rightarrow x = \frac{1}{3}

The

x

-intercept is the coordinate value where the graph intersects the

x

-axis, which mathematically occurs when

y = 0

Determining the equation of a line from tabular coordinates and calculating its intercepts

Question