Question

a line passes through the points (3, 7) and (5, 7). 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 formula is $m=\frac{y_2-y_1}{x_2-x_1}$. Substitute $(x_1,y_1)=(3,7)$ and $(x_2,y_2)=(5,7)$:
$m=\frac{7-7}{5-3}=\frac{0}{2}=0$

Step2: Identify y-intercept

Since the line is horizontal (slope=0), it passes through $y=7$ for all x, so the y-intercept $b=7$.

Step3: Write slope-intercept form

Slope-intercept form is $y=mx+b$. Substitute $m=0$ and $b=7$:
$y=0x+7$ which simplifies to $y=7$

Answer:

$y=7$