Question

1. slope

y-intercept (b) =
equation:
grid with a line

Explanation:

Step1: Find two points on the line

From the graph, we can identify two points: \((2, 0)\) and \((0, -1)\) (the y - intercept point).

Step2: Calculate the slope (m)

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

Step3: Identify the y - intercept (b)

The y - intercept is the value of \(y\) when \(x = 0\). From the point \((0,-1)\), we get \(b=-1\).

Step4: Write the equation of the line

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

Answer:

slope \(=\frac{1}{2}\), y - intercept \((b)=-1\), equation: \(y = \frac{1}{2}x-1\)