Question

m= b=-3 eq: y=

Explanation:

Step1: Determine the slope (m)

To find the slope \( m \), we can use two points on the line. From the graph, we can see that the line passes through \((0, -3)\) (the y - intercept) and another point, say \((4, -1)\) (by counting the grid). The slope formula is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Using \((x_1,y_1)=(0, - 3)\) and \((x_2,y_2)=(4, - 1)\), we have \( m=\frac{-1-(-3)}{4 - 0}=\frac{-1 + 3}{4}=\frac{2}{4}=\frac{1}{2} \).

Step2: Use the slope - intercept form

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 \( m=\frac{1}{2} \) and \( b=-3 \). Substituting these values into the formula, we get \( y=\frac{1}{2}x-3 \).

Answer:

\( m = \frac{1}{2} \), the equation of the line is \( y=\frac{1}{2}x - 3 \)