Question

find the slope of each line and write the equation of each graph.
9.
10.

Explanation:

Problem 9

Step 1: Identify two points

From the graph, we can see that the line passes through \((-5, -1)\) and \((0, -2)\) (or other clear points). Let's use \((x_1, y_1)=(-5, -1)\) and \((x_2, y_2)=(0, -2)\).

Step 2: Calculate the slope

The slope formula is \(m = \frac{y_2 - y_1}{x_2 - x_1}\).
Substituting the values: \(m=\frac{-2 - (-1)}{0 - (-5)}=\frac{-2 + 1}{5}=\frac{-1}{5}=-\frac{1}{5}\)

Step 3: Find the equation

The y - intercept \(b\) is the value of \(y\) when \(x = 0\). From the point \((0, -2)\), \(b=-2\).
The slope - intercept form of a line is \(y=mx + b\). Substituting \(m =-\frac{1}{5}\) and \(b=-2\), we get \(y=-\frac{1}{5}x-2\)

Step 1: Identify two points

From the graph, the line passes through \((-5, 0)\) and \((0, 1)\) (or other clear points). Let \((x_1, y_1)=(-5, 0)\) and \((x_2, y_2)=(0, 1)\)

Step 2: Calculate the slope

Using the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\)
Substituting the values: \(m=\frac{1 - 0}{0 - (-5)}=\frac{1}{5}\)

Step 3: Find the equation

The y - intercept \(b\) is the value of \(y\) when \(x = 0\). From the point \((0, 1)\), \(b = 1\)
Using the slope - intercept form \(y=mx + b\) with \(m=\frac{1}{5}\) and \(b = 1\), we get \(y=\frac{1}{5}x+1\)

Answer:

Slope: \(-\frac{1}{5}\), Equation: \(y =-\frac{1}{5}x - 2\)

Problem 10