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 \((x_1,y_1)\) and \((x_2,y_2)\). From the graph, we can take \((- 10,0)\) and \((0,-5)\)

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting the points \((-10,0)\) and \((0,-5)\) gives \(m=\frac{-5 - 0}{0-(-10)}=\frac{-5}{10}=-\frac{1}{2}\)

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

The y - intercept is the y - value when \(x = 0\). From the point \((0,-5)\), \(b=-5\)

Step4: Write the equation in slope - intercept form

The slope - intercept form of a line is \(y=mx + b\). Substituting \(m =-\frac{1}{2}\) and \(b=-5\) gives \(y=-\frac{1}{2}x-5\)

Answer:

\(y =-\frac{1}{2}x - 5\)