Question

write the equation from each line
1)
2)
3)
4)
5)
6)
7)
8)

Explanation:

Let's solve the first problem (1) to find the equation of the line.

Step 1: Identify two points on the line

Looking at the graph for problem 1, we can see that the line passes through \((0, -5)\) (the y - intercept) and \((1, -3)\) (we can find another point by moving 1 unit right and 2 units up from the y - intercept).

Step 2: Calculate the slope (\(m\))

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0, - 5)\) and \((x_2,y_2)=(1, - 3)\). Then \(m=\frac{-3-(-5)}{1 - 0}=\frac{-3 + 5}{1}=\frac{2}{1}=2\).

Step 3: Use the slope - intercept form (\(y=mx + b\))

The slope - intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. We know that \(m = 2\) and from the point \((0,-5)\), the y - intercept \(b=-5\). So the equation of the line is \(y=2x-5\).

Answer:

For problem 1, the equation of the line is \(y = 2x-5\)

(If you want solutions for other problems, please provide more details about the coordinates of the points on the lines or describe the graphs more precisely, such as the slope and y - intercept for each line.)