Question

question write the equation of the line in fully simplified slope - intercept form.

Explanation:

Step1: Identify two points on the line

Let's assume two points on the line are \((x_1,y_1)\) and \((x_2,y_2)\). From the graph, we can take \((- 4,0)\) and \((0,2)\)

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting the points \((-4,0)\) and \((0,2)\) gives \(m=\frac{2 - 0}{0-(-4)}=\frac{2}{4}=\frac{1}{2}\)

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

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

Step4: Write the equation in slope - intercept form

The slope - intercept form is \(y=mx + b\). Substituting \(m=\frac{1}{2}\) and \(b = 2\) gives \(y=\frac{1}{2}x+2\)

Answer:

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