Question

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

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.

Step2: Find the y - intercept (\(b\))

The y - intercept is the point where the line crosses the y - axis. From the graph, the line crosses the y - axis at \((0,-6)\), so \(b=-6\).

Step3: Calculate the slope (\(m\))

We can use two points on the line to calculate the slope. Let's take two points: \((0, - 6)\) and \((8,-5)\) (we can also use other points, but these are easy to identify). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substituting \(x_1 = 0,y_1=-6,x_2 = 8,y_2=-5\) into the formula:
\(m=\frac{-5-(-6)}{8 - 0}=\frac{-5 + 6}{8}=\frac{1}{8}\)

Step4: Write the equation

Substitute \(m=\frac{1}{8}\) and \(b = - 6\) into the slope - intercept form \(y=mx + b\).
We get \(y=\frac{1}{8}x-6\)

Answer:

\(y=\frac{1}{8}x - 6\)