Question

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

Explanation:

Step1: Identify two points on the line

Let's take two clear - cut points, say (- 8,-2) and (8,0).

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting \(x_1=-8,y_1 = - 2,x_2 = 8,y_2=0\) into the formula, we get \(m=\frac{0-(-2)}{8 - (-8)}=\frac{2}{16}=\frac{1}{8}\).

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

The slope - intercept form of a line is \(y=mx + b\). We know \(m=\frac{1}{8}\), and we can use the point (8,0). Substitute \(x = 8,y = 0,m=\frac{1}{8}\) into \(y=mx + b\): \(0=\frac{1}{8}\times8+b\), which simplifies to \(0 = 1 + b\), so \(b=-1\).

Step4: Write the equation of the line

Substitute \(m=\frac{1}{8}\) and \(b=-1\) into \(y=mx + b\), we get \(y=\frac{1}{8}x-1\).

Answer:

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