Question

write the equation of this line in slope - intercept form. write your answer using integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Identify two points on the line

Let's take two points \((0,0)\) and \((1,4)\) from the graph.

Step2: Calculate the slope \(m\)

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

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

The line crosses the y - axis at \((0,0)\), so \(b = 0\).

Step4: Write the equation in slope - intercept form

The slope - intercept form is \(y=mx + b\). Substituting \(m = 4\) and \(b = 0\), we get \(y = 4x+0\) or simply \(y = 4x\).

Answer:

\(y = 4x\)