Question

question
write the equation of the line in fully simplified slope - intercept form.
q2 delta #9
date: december 8 at 8:00 am
grade: 13%
graphing lines from equations
writing equations of lines
table to linear equation (level 1)
scientific calculator
graphing calculator
jordan sheriff
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Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through \((-6, 0)\) and \((6, -6)\) (we can also use other points, but these are clear).

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(-6, 0)\) and \((x_2,y_2)=(6, -6)\). Then \(m=\frac{-6 - 0}{6 - (-6)}=\frac{-6}{12}=-\frac{1}{2}\).

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

We use the slope - intercept form \(y = mx + b\). We know \(m =-\frac{1}{2}\) and we can use the point \((-6, 0)\). Substitute \(x=-6\), \(y = 0\) and \(m=-\frac{1}{2}\) into \(y=mx + b\):
\(0=-\frac{1}{2}(-6)+b\)
\(0 = 3 + b\)
Subtract 3 from both sides: \(b=-3\).

Step4: Write the equation

The slope - intercept form is \(y=mx + b\). Substituting \(m =-\frac{1}{2}\) and \(b=-3\), we get \(y=-\frac{1}{2}x-3\).

Answer:

\(y =-\frac{1}{2}x - 3\)