Question

1. (graph of a line segment on a coordinate grid with x from 0 to 10 and y from 0 to 10, points at (4,9) and (6,7))

Explanation:

To solve the problem related to the line segment on the coordinate grid (likely finding the slope or equation of the line), we can follow these steps:

Step 1: Identify the coordinates of the two points

From the graph, the two points are:

• Point 1: \((4, 9)\) (where \(x_1 = 4\) and \(y_1 = 9\))
• Point 2: \((6, 7)\) (where \(x_2 = 6\) and \(y_2 = 7\))

Step 2: Calculate the slope (\(m\)) of the line segment

The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substitute the values of \(x_1, y_1, x_2,\) and \(y_2\) into the formula:
\[
m = \frac{7 - 9}{6 - 4} = \frac{-2}{2} = -1
\]

Step 3: (Optional) Find the equation of the line (using point - slope form)

The point - slope form of a line is \(y - y_1=m(x - x_1)\). Using the point \((4, 9)\) and \(m=-1\):
\[
y - 9=-1(x - 4)
\]
Simplify the equation:
\[
y - 9=-x + 4
\]
\[
y=-x + 13
\]

If the question was to find the slope of the line segment joining the points \((4,9)\) and \((6,7)\):

Answer:

The slope of the line segment is \(-1\)

If the question was to find the equation of the line: