Question

The graph of a proportional linear equation has a slope of −2
and passes through the point (−2,4)
. Supply the numbers that complete the ordered pairs that are also contained on the same line.(1 point)
(−3,
), (4,
)

Answer 1

Given a proportional linear equation with a slope of -2 and passing through the point (-2, 4), we can use the point-slope form of the linear equation to find the other points on the line.

The slope-intercept form of the linear equation is given by:

\[ y = mx + b \]

where \( m \) is the slope and \( b \) is the y-intercept. However, since the equation is proportional, it can be expressed in a form that goes through the origin without a y-intercept.

Start with the general form of the line using the point-slope equation:

\[ y - y_1 = m(x - x_1) \]

Substituting the slope \( m = -2 \) and the point \( (-2, 4) \):

\[ y - 4 = -2(x + 2) \]

Now simplify this equation:

\[ y - 4 = -2x - 4 \]

\[ y = -2x \]

Now we can find the missing values in the ordered pairs (−3, y) and (4, y).

1. For (−3, y):

Substitute \( x = -3 \) into the equation:

\[ y = -2(-3) = 6 \]

So, the ordered pair is (−3, 6).

2. For (4, y):

Substitute \( x = 4 \) into the equation:

\[ y = -2(4) = -8 \]

So, the ordered pair is (4, -8).

Thus, the completed ordered pairs are:

(−3, 6) and (4, -8).