Question

1. slope (m) =

y-intercept (b) =
equation: y =

Explanation:

Step1: Find two points on the line

Looking at the graph, the line passes through \((0, 0)\) and \((2, 1)\) (we can also use other points, but these are clear).

Step2: Calculate the slope \(m\)

The formula for slope is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using \((x_1,y_1)=(0,0)\) and \((x_2,y_2)=(2,1)\), we get \(m = \frac{1 - 0}{2 - 0}=\frac{1}{2}\).

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

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

Step4: Write the equation of the line

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

Answer:

slope (\(m\)) = \(\frac{1}{2}\)
y - intercept (\(b\)) = \(0\)
equation: \(y=\frac{1}{2}x\)