Question

1. y =

m = b =

Explanation:

Step1: Identify two points on the line

From the graph, we can see two points: \((0, 2)\) (the y - intercept) and \((-3, -4)\).

Step2: Calculate the slope \(m\)

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0,2)\) and \((x_2,y_2)=(-3,-4)\). Then \(m=\frac{-4 - 2}{-3 - 0}=\frac{-6}{-3}=2\).

Step3: Identify the y - intercept \(b\)

The y - intercept \(b\) is the value of \(y\) when \(x = 0\). From the point \((0,2)\), we can see that \(b = 2\).

Step4: Write the equation of the line

The slope - intercept form of a line is \(y=mx + b\). Substituting \(m = 2\) and \(b = 2\) into the formula, we get \(y=2x + 2\).

Answer:

\(y = 2x+2\), \(m = 2\), \(b = 2\)