Question

determine the slope of the linear relations using the information provided.

x	y
-1	-5
0	-1
1	3
2	7

graph with points plotted passes through the points (4, 2) and (- 2, 2).

$y = \frac{4}{5}x + 3$

Explanation:

1. Slope from the table (points \((-2, -9)\) and \((-1, -5)\))

Step1: Recall slope formula

The slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1, y_1)=(-2, -9)\) and \((x_2, y_2)=(-1, -5)\).

Step2: Substitute values

\(m=\frac{-5 - (-9)}{-1 - (-2)}=\frac{-5 + 9}{-1 + 2}=\frac{4}{1}=4\).

2. Slope from the graph (assuming two points, say \((-2, 3)\) and \((1, 1)\))

Step1: Identify two points

From the graph, let's take \((x_1, y_1)=(-2, 3)\) and \((x_2, y_2)=(1, 1)\).

Step2: Apply slope formula

\(m=\frac{1 - 3}{1 - (-2)}=\frac{-2}{3}=-\frac{2}{3}\). (Note: The exact points depend on the graph's coordinates, but this is a general approach.)

3. Slope from points \((4, 2)\) and \((-2, 2)\)

Step1: Use slope formula

Let \((x_1, y_1)=(4, 2)\) and \((x_2, y_2)=(-2, 2)\). Then \(m=\frac{2 - 2}{-2 - 4}=\frac{0}{-6}=0\).

4. Slope from the equation \(y = \frac{4}{5}x + 3\)

Answer:

s:

• Slope from the table: \(4\)
• Slope from the graph (approximate, depending on points): \(-\frac{2}{3}\) (or other value based on exact graph points)
• Slope from points \((4,2)\) and \((-2,2)\): \(0\)
• Slope from \(y=\frac{4}{5}x + 3\): \(\frac{4}{5}\)