Question

a line passes through the points (6, 15) and (12, 15). write its equation in slope - intercept form. write your answer using integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Calculate the slope

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Here, \((x_1, y_1)=(6, 15)\) and \((x_2, y_2)=(12, 15)\). So \( m=\frac{15 - 15}{12 - 6}=\frac{0}{6} = 0 \).

Step2: Use slope - intercept form \( y=mx + b \)

We know \( m = 0 \) and we can use one of the points, say \((6,15)\), to find \( b \). Substitute \( x = 6 \), \( y = 15 \) and \( m = 0 \) into \( y=mx + b \):
\( 15=0\times6 + b \)
\( 15 = b \)

Step3: Write the equation

The slope - intercept form is \( y=mx + b \). Substituting \( m = 0 \) and \( b = 15 \), we get \( y=0x + 15 \), which simplifies to \( y = 15 \).

Answer:

\( y = 15 \)