Question

a line passes through the points (1, 1) and (2, 8). 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 $m=\frac{y_2-y_1}{x_2-x_1}$. For points $(1,1)$ and $(2,8)$, substitute values:
$m=\frac{8-1}{2-1}=\frac{7}{1}=7$

Step2: Find y-intercept $b$

Use slope-intercept form $y=mx+b$, substitute $m=7$, $x=1$, $y=1$:
$1=7(1)+b$
Solve for $b$:
$b=1-7=-6$

Step3: Write final equation

Substitute $m=7$ and $b=-6$ into $y=mx+b$:
$y=7x-6$

Answer:

$y=7x-6$