Question

slope intercept form
write the equation for the line.
y = mx + b
y = x +

Explanation:

Step1: Identify two points on the line

Looking at the graph, we can pick two clear points. Let's take \((-4, -3)\) and \((2, 0)\) (we can also use other points, but these are easy to identify).

Step2: Calculate the slope \(m\)

The formula for slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substituting \((x_1, y_1)=(-4, -3)\) and \((x_2, y_2)=(2, 0)\):
\(m=\frac{0 - (-3)}{2 - (-4)}=\frac{3}{6}=\frac{1}{2}\)

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

We can use the point - slope form or just look at where the line crosses the y - axis. Let's use the slope - intercept form \(y = mx + b\) and substitute one of the points. Let's use the point \((2, 0)\) and \(m=\frac{1}{2}\).
Substitute into \(y=mx + b\): \(0=\frac{1}{2}(2)+b\)
Simplify: \(0 = 1 + b\), so \(b=-1\)

Answer:

\(y=\frac{1}{2}x-1\)